diff --git a/README.md b/README.md index a94f534..19a733a 100644 --- a/README.md +++ b/README.md @@ -5,7 +5,7 @@ Fast 3d math library for webgpu * [Docs](https://wgpu-matrix.org/docs) -* [Repo](https://github.com/greggman/wgpu-matrix) +* [Github](https://github.com/greggman/wgpu-matrix) * [Tests](https://wgpu-matrix.org/test/) ## Why another 3d math library? @@ -146,6 +146,80 @@ import {vec3, mat3} from 'wgpu-matrix'; * [tar](https://github.com/greggman/wgpu-matrix/tarball/main) * [github](https://github.com/greggman/wgpu-matrix) +## Types + +### wgpu-matrix functions take any compatible type as input. + +Examples: + +```ts +const view = mat4.lookAt( // view is Float32Array + [10, 20, 30], // position + [0, 5, 0], // target + [0, 1, 0], // up +); + +const view2 = mat4.lookAt( // view2 is Float32Array + new Float32Array([10, 20, 30]), // position + new Float64Array([0, 5, 0], // target + [0, 1, 0], // up +); +``` + +### wgpu-matrix functions return the type passed as the destination or their default + +```ts +const a = vec2.add([1, 2], [3, 4]); // a is Float32Array +const b = vec2.add([1, 2], [3, 4], [0, 0]); // b is number[] + +const j = vec2d.add([1, 2], [3, 4]); // j is Float64Array +const k = vec2d.add([1, 2], [3, 4], [0, 0]); // b is number[] + +const f32 = new Float32Array(2); +const x = vec2d.add([1, 2], [3, 4]); // x is number[] +const y = vec2d.add([1, 2], [3, 4], f32); // y is Float32Array +``` + +etc... + +Note: You're unlikely to need any thing except `mat3`, `mat4`, `quat`, +`vec2`, `vec3`, and `vec4` but, there are 3 sets of functions, +each one returning a different default + +```ts +mat4.identity() // returns Float32Array +mat4d.identity() // returns Float64Array +mat4n.identity() // returns number[] +``` + +Similarly there's `mat3d`, `mat3n`, `quatd`, `quatn`, +`vec2d`, `vec2n`, `vec3d`, `vec3n`, `vec4d`, `vec4n`. + +Just to be clear, `identity`, like most functions, takes a destination so + +```ts +const f32 = new Float32Array(16); +const f64 = new Float64Array(16); +const arr = new Array(16).fill(0); + +mat4.identity() // returns Float32Array +mat4.identity(f32) // returns Float32Array (f32) +mat4.identity(f64) // returns Float64Array (f64) +mat4.identity(arr) // returns number[] (arr) + +mat4d.identity() // returns Float64Array +mat4d.identity(f32) // returns Float32Array (f32) +mat4d.identity(f64) // returns Float64Array (f64) +mat4d.identity(arr) // returns number[] (arr) + +mat4n.identity() // returns number[] +mat4n.identity(f32) // returns Float32Array (f32) +mat4n.identity(f64) // returns Float64Array (f64) +mat4n.identity(arr) // returns number[] (arr) +``` + +The only difference between the sets of functions is what type they default to returning. + ## Notes [`mat4.perspective`](https://wgpu-matrix.org/docs/functions/mat4.perspective.html), @@ -276,11 +350,11 @@ a destination it returns the type of the destination ```ts mat4.identity() // returns Float32Array mat4.identity(new Float32Array(16)); // returns Float32Array -mat4.identity(new Float64Array(16)); // returns Float32Array +mat4.identity(new Float64Array(16)); // returns Float64Array mat4.identity(new Array(16)); // returns number[] ``` -### Types are specific +#### Types are specific ```ts const a: Mat4 = ...; // a = Float32Array @@ -313,7 +387,7 @@ If you really want types for each concrete type there's * `Float64Array` types: `Mat3d`, `Mat4d`, `Quatd`, `Vec2d`, `Vec3d`, `Vec4d`, * `number[]` types: `Mat3n`, `Mat4n`, `Quatn`, `Vec2n`, `Vec3n`, `Vec4n` -### There are 3 sets of functions, each one returning a different default +#### There are 3 sets of functions, each one returning a different default ```ts mat4.identity() // returns Float32Array diff --git a/dist/3.x/wgpu-matrix.d.ts b/dist/3.x/wgpu-matrix.d.ts index 6072c3a..96a7269 100644 --- a/dist/3.x/wgpu-matrix.d.ts +++ b/dist/3.x/wgpu-matrix.d.ts @@ -1,3 +1,7 @@ +/** + * Some docs + * @namespace wgpu-matrix + */ import { BaseArgType } from './types'; import { Mat3Arg, Mat3Type } from './mat3-impl'; import { Mat4Arg, Mat4Type } from './mat4-impl'; @@ -27,7 +31,10 @@ export type Vec2n = Vec2Type; export type Vec3n = Vec3Type; export type Vec4n = Vec4Type; export declare const -/** @namespace */ +/** + * 4x4 Matrix functions that default to returning `Float32Array` + * @namespace + */ mat4: { create: (v0?: number | undefined, v1?: number | undefined, v2?: number | undefined, v3?: number | undefined, v4?: number | undefined, v5?: number | undefined, v6?: number | undefined, v7?: number | undefined, v8?: number | undefined, v9?: number | undefined, v10?: number | undefined, v11?: number | undefined, v12?: number | undefined, v13?: number | undefined, v14?: number | undefined, v15?: number | undefined) => Float32Array; set: (v0: number, v1: number, v2: number, v3: number, v4: number, v5: number, v6: number, v7: number, v8: number, v9: number, v10: number, v11: number, v12: number, v13: number, v14: number, v15: number, dst?: T | undefined) => T; @@ -75,7 +82,10 @@ mat4: { uniformScaling: (s: number, dst?: T_34 | undefined) => T_34; uniformScale: (m: BaseArgType, s: number, dst?: T_35 | undefined) => T_35; }, -/** @namespace */ +/** + * 3x3 Matrix functions that default to returning `Float32Array` + * @namespace + */ mat3: { clone: (m: BaseArgType, dst?: T | undefined) => T; create: (v0?: number | undefined, v1?: number | undefined, v2?: number | undefined, v3?: number | undefined, v4?: number | undefined, v5?: number | undefined, v6?: number | undefined, v7?: number | undefined, v8?: number | undefined) => Float32Array; @@ -107,7 +117,10 @@ mat3: { uniformScaling: (s: number, dst?: T_20 | undefined) => T_20; uniformScale: (m: BaseArgType, s: number, dst?: T_21 | undefined) => T_21; }, -/** @namespace */ +/** + * Quaternion functions that default to returning `Float32Array` + * @namespace + */ quat: { create: (x?: number | undefined, y?: number | undefined, z?: number | undefined, w?: number | undefined) => Float32Array; fromValues: (x?: number | undefined, y?: number | undefined, z?: number | undefined, w?: number | undefined) => Float32Array; @@ -149,7 +162,10 @@ quat: { rotationTo: (aUnit: BaseArgType, bUnit: BaseArgType, dst?: T_20 | undefined) => T_20; sqlerp: (a: BaseArgType, b: BaseArgType, c: BaseArgType, d: BaseArgType, t: number, dst?: T_21 | undefined) => T_21; }, -/** @namespace */ +/** + * Vec2 functions that default to returning `Float32Array` + * @namespace + */ vec2: { create: (x?: number, y?: number) => Float32Array; fromValues: (x?: number, y?: number) => Float32Array; @@ -201,7 +217,10 @@ vec2: { truncate: (a: BaseArgType, maxLen: number, dst?: T_27 | undefined) => T_27; midpoint: (a: BaseArgType, b: BaseArgType, dst?: T_28 | undefined) => T_28; }, -/** @namespace */ +/** + * Vec3 functions that default to returning `Float32Array` + * @namespace + */ vec3: { create: (x?: number | undefined, y?: number | undefined, z?: number | undefined) => Float32Array; fromValues: (x?: number | undefined, y?: number | undefined, z?: number | undefined) => Float32Array; @@ -260,7 +279,10 @@ vec3: { truncate: (a: BaseArgType, maxLen: number, dst?: T_34 | undefined) => T_34; midpoint: (a: BaseArgType, b: BaseArgType, dst?: T_35 | undefined) => T_35; }, -/** @namespace */ +/** + * Vec3 functions that default to returning `Float32Array` + * @namespace + */ vec4: { create: (x?: number | undefined, y?: number | undefined, z?: number | undefined, w?: number | undefined) => Float32Array; fromValues: (x?: number | undefined, y?: number | undefined, z?: number | undefined, w?: number | undefined) => Float32Array; diff --git a/dist/3.x/wgpu-matrix.js b/dist/3.x/wgpu-matrix.js index 4218068..6082b38 100644 --- a/dist/3.x/wgpu-matrix.js +++ b/dist/3.x/wgpu-matrix.js @@ -1,4 +1,4 @@ -/* wgpu-matrix@3.0.1, license MIT */ +/* wgpu-matrix@3.0.2, license MIT */ (function (global, factory) { typeof exports === 'object' && typeof module !== 'undefined' ? factory(exports) : typeof define === 'function' && define.amd ? define(['exports'], factory) : @@ -4684,7 +4684,7 @@ newDst[0] = 0; newDst[1] = 0; newDst[2] = 0; - newDst[3] = 0; + newDst[3] = 1; } return newDst; } @@ -5537,6 +5537,10 @@ return api; } + /** + * Some docs + * @namespace wgpu-matrix + */ /** * Generate wgpu-matrix API for type */ @@ -5557,43 +5561,97 @@ }; } const { - /** @namespace */ + /** + * 4x4 Matrix functions that default to returning `Float32Array` + * @namespace + */ mat4, - /** @namespace */ + /** + * 3x3 Matrix functions that default to returning `Float32Array` + * @namespace + */ mat3, - /** @namespace */ + /** + * Quaternion functions that default to returning `Float32Array` + * @namespace + */ quat, - /** @namespace */ + /** + * Vec2 functions that default to returning `Float32Array` + * @namespace + */ vec2, - /** @namespace */ + /** + * Vec3 functions that default to returning `Float32Array` + * @namespace + */ vec3, - /** @namespace */ + /** + * Vec3 functions that default to returning `Float32Array` + * @namespace + */ vec4, } = wgpuMatrixAPI(Float32Array, Float32Array, Float32Array, Float32Array, Float32Array, Float32Array); const { - /** @namespace */ + /** + * 4x4 Matrix functions that default to returning `Float64Array` + * @namespace + */ mat4: mat4d, - /** @namespace */ + /** + * 3x3 Matrix functions that default to returning `Float64Array` + * @namespace + */ mat3: mat3d, - /** @namespace */ + /** + * Quaternion functions that default to returning `Float64Array` + * @namespace + */ quat: quatd, - /** @namespace */ + /** + * Vec2 functions that default to returning `Float64Array` + * @namespace + */ vec2: vec2d, - /** @namespace */ + /** + * Vec3 functions that default to returning `Float64Array` + * @namespace + */ vec3: vec3d, - /** @namespace */ + /** + * Vec3 functions that default to returning `Float64Array` + * @namespace + */ vec4: vec4d, } = wgpuMatrixAPI(Float64Array, Float64Array, Float64Array, Float64Array, Float64Array, Float64Array); const { - /** @namespace */ + /** + * 4x4 Matrix functions that default to returning `number[]` + * @namespace + */ mat4: mat4n, - /** @namespace */ + /** + * 3x3 Matrix functions that default to returning `number[]` + * @namespace + */ mat3: mat3n, - /** @namespace */ + /** + * Quaternion functions that default to returning `number[]` + * @namespace + */ quat: quatn, - /** @namespace */ + /** + * Vec2 functions that default to returning `number[]` + * @namespace + */ vec2: vec2n, - /** @namespace */ + /** + * Vec3 functions that default to returning `number[]` + * @namespace + */ vec3: vec3n, - /** @namespace */ + /** + * Vec3 functions that default to returning `number[]` + * @namespace + */ vec4: vec4n, } = wgpuMatrixAPI(ZeroArray, Array, Array, Array, Array, Array); exports.mat3 = mat3; diff --git a/dist/3.x/wgpu-matrix.js.map b/dist/3.x/wgpu-matrix.js.map index 78f96bf..92061f6 100644 --- a/dist/3.x/wgpu-matrix.js.map +++ b/dist/3.x/wgpu-matrix.js.map @@ -1 +1 @@ -{"version":3,"file":"wgpu-matrix.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/mat3-impl.ts","../../../src/vec3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n translation,\n translate,\n rotation,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the dot product of two vectors\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec4Arg, b: Vec4Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return Math.sqrt(dx * dx + dy * dy + dz * dz + dw * dw);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return dx * dx + dy * dy + dz * dz + dw * dw;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n newDst[3] = -v[3];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec4.clone})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n newDst[3] = v[3];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec4.copy})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n newDst[3] = a[3] * b[3];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n newDst[3] = a[3] / b[3];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec4 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec4 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec4Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = v[3];\n\n newDst[0] = m[0] * x + m[4] * y + m[ 8] * z + m[12] * w;\n newDst[1] = m[1] * x + m[5] * y + m[ 9] * z + m[13] * w;\n newDst[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;\n newDst[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;\n\n return newDst;\n}\n\n\n/**\n * Treat a 4D vector as a direction and set it's length\n *\n * @param a The vec4 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec4Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec4 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec4Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n zero,\n transformMat4,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Vec4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Vec4`. In other words you can do this\n *\n * const v = vec4.cross(v1, v2); // Creates a new Vec4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec4.create();\n * vec4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * vec4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: Vec4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n\n","import {BaseArgType, ZeroArray} from './types';\nimport {Mat3Arg, Mat3Type, getAPI as getMat3API} from './mat3-impl';\nimport {Mat4Arg, Mat4Type, getAPI as getMat4API} from './mat4-impl';\nimport {QuatArg, QuatType, getAPI as getQuatAPI, RotationOrder} from './quat-impl';\nimport {Vec2Arg, Vec2Type, getAPI as getVec2API} from './vec2-impl';\nimport {Vec3Arg, Vec3Type, getAPI as getVec3API} from './vec3-impl';\nimport {Vec4Arg, Vec4Type, getAPI as getVec4API} from './vec4-impl';\nimport * as utils from './utils';\n\nexport {\n RotationOrder,\n utils,\n\n BaseArgType,\n\n Mat3Arg,\n Mat4Arg,\n QuatArg,\n Vec2Arg,\n Vec3Arg,\n Vec4Arg,\n\n Mat3Type,\n Mat4Type,\n QuatType,\n Vec2Type,\n Vec3Type,\n Vec4Type,\n};\n\nexport type BaseCtor = new (n: number) => T;\n\nexport type Mat3 = Mat3Type;\nexport type Mat4 = Mat4Type;\nexport type Quat = QuatType;\nexport type Vec2 = Vec2Type;\nexport type Vec3 = Vec3Type;\nexport type Vec4 = Vec4Type;\n\nexport type Mat3d = Mat3Type;\nexport type Mat4d = Mat4Type;\nexport type Quatd = QuatType;\nexport type Vec2d = Vec2Type;\nexport type Vec3d = Vec3Type;\nexport type Vec4d = Vec4Type;\n\nexport type Mat3n = Mat3Type;\nexport type Mat4n = Mat4Type;\nexport type Quatn = QuatType;\nexport type Vec2n = Vec2Type;\nexport type Vec3n = Vec3Type;\nexport type Vec4n = Vec4Type;\n\n/**\n * Generate wgpu-matrix API for type\n */\nfunction wgpuMatrixAPI<\n Mat3 extends BaseArgType,\n Mat4 extends BaseArgType,\n Quat extends BaseArgType,\n Vec2 extends BaseArgType,\n Vec3 extends BaseArgType,\n Vec4 extends BaseArgType,\n>(\n Mat3Ctor: BaseCtor,\n Mat4Ctor: BaseCtor,\n QuatCtor: BaseCtor,\n Vec2Ctor: BaseCtor,\n Vec3Ctor: BaseCtor,\n Vec4Ctor: BaseCtor,\n) {\n return {\n /** @namespace mat4 */\n mat4: getMat4API(Mat3Ctor),\n /** @namespace mat3 */\n mat3: getMat3API(Mat4Ctor),\n /** @namespace quat */\n quat: getQuatAPI(QuatCtor),\n /** @namespace vec2 */\n vec2: getVec2API(Vec2Ctor),\n /** @namespace vec3 */\n vec3: getVec3API(Vec3Ctor),\n /** @namespace vec4 */\n vec4: getVec4API(Vec4Ctor),\n };\n}\n\nexport const {\n /** @namespace */\n mat4,\n /** @namespace */\n mat3,\n /** @namespace */\n quat,\n /** @namespace */\n vec2,\n /** @namespace */\n vec3,\n /** @namespace */\n vec4,\n} = wgpuMatrixAPI<\n Mat3, Mat4, Quat, Vec2, Vec3, Vec4>(\n Float32Array, Float32Array, Float32Array, Float32Array, Float32Array, Float32Array);\n\nexport const {\n /** @namespace */\n mat4: mat4d,\n /** @namespace */\n mat3: mat3d,\n /** @namespace */\n quat: quatd,\n /** @namespace */\n vec2: vec2d,\n /** @namespace */\n vec3: vec3d,\n /** @namespace */\n vec4: vec4d,\n} = wgpuMatrixAPI<\n Mat3d, Mat4d, Quatd, Vec2d, Vec3d, Vec4d>(\n Float64Array, Float64Array, Float64Array, Float64Array, Float64Array, Float64Array);\n\nexport const {\n /** @namespace */\n mat4: mat4n,\n /** @namespace */\n mat3: mat3n,\n /** @namespace */\n quat: quatn,\n /** @namespace */\n vec2: vec2n,\n /** @namespace */\n vec3: vec3n,\n /** @namespace */\n vec4: vec4n,\n} = wgpuMatrixAPI<\n Mat3n, Mat4n, Quatn, Vec2n, Vec3n, Vec4n>(\n ZeroArray, Array, Array, Array, Array, 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\ No newline at end of file +{"version":3,"file":"wgpu-matrix.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/mat3-impl.ts","../../../src/vec3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n translation,\n translate,\n rotation,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the dot product of two vectors\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec4Arg, b: Vec4Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return Math.sqrt(dx * dx + dy * dy + dz * dz + dw * dw);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return dx * dx + dy * dy + dz * dz + dw * dw;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n newDst[3] = -v[3];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec4.clone})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n newDst[3] = v[3];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec4.copy})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n newDst[3] = a[3] * b[3];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n newDst[3] = a[3] / b[3];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec4 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec4 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec4Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = v[3];\n\n newDst[0] = m[0] * x + m[4] * y + m[ 8] * z + m[12] * w;\n newDst[1] = m[1] * x + m[5] * y + m[ 9] * z + m[13] * w;\n newDst[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;\n newDst[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;\n\n return newDst;\n}\n\n\n/**\n * Treat a 4D vector as a direction and set it's length\n *\n * @param a The vec4 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec4Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec4 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec4Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n zero,\n transformMat4,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Vec4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Vec4`. In other words you can do this\n *\n * const v = vec4.cross(v1, v2); // Creates a new Vec4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec4.create();\n * vec4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. 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Vec2Type,\n Vec3Type,\n Vec4Type,\n};\n\nexport type BaseCtor = new (n: number) => T;\n\nexport type Mat3 = Mat3Type;\nexport type Mat4 = Mat4Type;\nexport type Quat = QuatType;\nexport type Vec2 = Vec2Type;\nexport type Vec3 = Vec3Type;\nexport type Vec4 = Vec4Type;\n\nexport type Mat3d = Mat3Type;\nexport type Mat4d = Mat4Type;\nexport type Quatd = QuatType;\nexport type Vec2d = Vec2Type;\nexport type Vec3d = Vec3Type;\nexport type Vec4d = Vec4Type;\n\nexport type Mat3n = Mat3Type;\nexport type Mat4n = Mat4Type;\nexport type Quatn = QuatType;\nexport type Vec2n = Vec2Type;\nexport type Vec3n = Vec3Type;\nexport type Vec4n = Vec4Type;\n\n/**\n * Generate wgpu-matrix API for type\n */\nfunction wgpuMatrixAPI<\n Mat3 extends BaseArgType,\n Mat4 extends BaseArgType,\n Quat extends BaseArgType,\n Vec2 extends BaseArgType,\n Vec3 extends BaseArgType,\n Vec4 extends BaseArgType,\n>(\n Mat3Ctor: BaseCtor,\n Mat4Ctor: BaseCtor,\n QuatCtor: BaseCtor,\n Vec2Ctor: BaseCtor,\n Vec3Ctor: BaseCtor,\n Vec4Ctor: BaseCtor,\n) {\n return {\n /** @namespace mat4 */\n mat4: getMat4API(Mat3Ctor),\n /** @namespace mat3 */\n mat3: getMat3API(Mat4Ctor),\n /** @namespace quat */\n quat: getQuatAPI(QuatCtor),\n /** @namespace vec2 */\n vec2: getVec2API(Vec2Ctor),\n /** @namespace vec3 */\n vec3: getVec3API(Vec3Ctor),\n /** @namespace vec4 */\n vec4: getVec4API(Vec4Ctor),\n };\n}\n\nexport const {\n /**\n * 4x4 Matrix functions that default to returning `Float32Array`\n * @namespace\n */\n mat4,\n /**\n * 3x3 Matrix functions that default to returning `Float32Array`\n * @namespace\n */\n mat3,\n /**\n * Quaternion functions that default to returning `Float32Array`\n * @namespace\n */\n quat,\n /**\n * Vec2 functions that default to returning `Float32Array`\n * @namespace\n */\n vec2,\n /**\n * Vec3 functions that default to returning `Float32Array`\n * @namespace\n */\n vec3,\n /**\n * Vec3 functions that default to returning `Float32Array`\n * @namespace\n */\n vec4,\n} = 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returning `number[]`\n * @namespace\n */\n mat4: mat4n,\n /**\n * 3x3 Matrix functions that default to returning `number[]`\n * @namespace\n */\n mat3: mat3n,\n /**\n * Quaternion functions that default to returning `number[]`\n * @namespace\n */\n quat: quatn,\n /**\n * Vec2 functions that default to returning `number[]`\n * @namespace\n */\n vec2: vec2n,\n /**\n * Vec3 functions that default to returning `number[]`\n * @namespace\n */\n vec3: vec3n,\n /**\n * Vec3 functions that default to returning `number[]`\n * @namespace\n */\n vec4: vec4n,\n} = wgpuMatrixAPI<\n Mat3n, Mat4n, Quatn, Vec2n, Vec3n, Vec4n>(\n ZeroArray, Array, Array, Array, Array, 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n(4);return c[0]=t[0]+r*(e[0]-t[0]),c[1]=t[1]+r*(e[1]-t[1]),c[2]=t[2]+r*(e[2]-t[2]),c[3]=t[3]+r*(e[3]-t[3]),c},length:v,len:p,lengthSq:q,lenSq:b,normalize:g,equalsApproximately:function(n,t){return Math.abs(n[0]-t[0]).999999?(u[0]=0,u[1]=0,u[2]=0,u[3]=1,u):(t.cross(e,r,x),u[0]=x[0],u[1]=x[1],u[2]=x[2],u[3]=1+a,g(u,u))},sqlerp:function(t,e,r,o,c,u){const a=u??new n(4);return s(t,o,c,S),s(e,r,c,z),s(S,z,2*c*(1-c),a),a}}}(n),w.set(n,t)),t}const d=new Map;function v(n){let t=d.get(n);return t||(t=function(n){function t(t,e,r,o){const c=new n(4);return void 0!==t&&(c[0]=t,void 0!==e&&(c[1]=e,void 0!==r&&(c[2]=r,void 0!==o&&(c[3]=o)))),c}function e(t,e,r){const o=r??new n(4);return o[0]=t[0]-e[0],o[1]=t[1]-e[1],o[2]=t[2]-e[2],o[3]=t[3]-e[3],o}function r(t,e,r,o){const c=o??new n(4);return c[0]=t[0]+r*(e[0]-t[0]),c[1]=t[1]+r*(e[1]-t[1]),c[2]=t[2]+r*(e[2]-t[2]),c[3]=t[3]+r*(e[3]-t[3]),c}function c(t,e,r){const o=r??new n(4);return o[0]=t[0]*e,o[1]=t[1]*e,o[2]=t[2]*e,o[3]=t[3]*e,o}function 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h(t,o),c(o,e,o)}return{create:t,fromValues:t,set:function(t,e,r,o,c){const u=c??new n(4);return u[0]=t,u[1]=e,u[2]=r,u[3]=o,u},ceil:function(t,e){const r=e??new n(4);return r[0]=Math.ceil(t[0]),r[1]=Math.ceil(t[1]),r[2]=Math.ceil(t[2]),r[3]=Math.ceil(t[3]),r},floor:function(t,e){const r=e??new n(4);return r[0]=Math.floor(t[0]),r[1]=Math.floor(t[1]),r[2]=Math.floor(t[2]),r[3]=Math.floor(t[3]),r},round:function(t,e){const r=e??new n(4);return r[0]=Math.round(t[0]),r[1]=Math.round(t[1]),r[2]=Math.round(t[2]),r[3]=Math.round(t[3]),r},clamp:function(t,e=0,r=1,o){const c=o??new n(4);return c[0]=Math.min(r,Math.max(e,t[0])),c[1]=Math.min(r,Math.max(e,t[1])),c[2]=Math.min(r,Math.max(e,t[2])),c[3]=Math.min(r,Math.max(e,t[3])),c},add:function(t,e,r){const o=r??new n(4);return o[0]=t[0]+e[0],o[1]=t[1]+e[1],o[2]=t[2]+e[2],o[3]=t[3]+e[3],o},addScaled:function(t,e,r,o){const c=o??new n(4);return c[0]=t[0]+e[0]*r,c[1]=t[1]+e[1]*r,c[2]=t[2]+e[2]*r,c[3]=t[3]+e[3]*r,c},subtract:e,sub:e,equalsApproximately:function(n,t){return Math.abs(n[0]-t[0])e?m(t,e,o):M(t,o)},midpoint:function(t,e,o){return r(t,e,.5,o??new n(4))}}}(n),d.set(n,t)),t}function p(n,t,e,r,o,c){return{mat4:l(n),mat3:i(t),quat:m(e),vec2:a(r),vec3:h(o),vec4:v(c)}}const{mat4:q,mat3:b,quat:g,vec2:x,vec3:y,vec4:A}=p(Float32Array,Float32Array,Float32Array,Float32Array,Float32Array,Float32Array),{mat4:S,mat3:z,quat:F,vec2:T,vec3:k,vec4:I}=p(Float64Array,Float64Array,Float64Array,Float64Array,Float64Array,Float64Array),{mat4:P,mat3:V,quat:Z,vec2:L,vec3:R,vec4:E}=p(t,Array,Array,Array,Array,Array);n.mat3=b,n.mat3d=z,n.mat3n=V,n.mat4=q,n.mat4d=S,n.mat4n=P,n.quat=g,n.quatd=F,n.quatn=Z,n.utils=c,n.vec2=x,n.vec2d=T,n.vec2n=L,n.vec3=y,n.vec3d=k,n.vec3n=R,n.vec4=A,n.vec4d=I,n.vec4n=E})); //# sourceMappingURL=wgpu-matrix.min.js.map diff --git a/dist/3.x/wgpu-matrix.min.js.map b/dist/3.x/wgpu-matrix.min.js.map index dba9693..a4a86e6 100644 --- a/dist/3.x/wgpu-matrix.min.js.map +++ b/dist/3.x/wgpu-matrix.min.js.map @@ -1 +1 @@ -{"version":3,"file":"wgpu-matrix.min.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/mat3-impl.ts","../../../src/vec3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n translation,\n translate,\n rotation,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. 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\ No newline at end of file +{"version":3,"file":"wgpu-matrix.min.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/mat3-impl.ts","../../../src/vec3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n translation,\n translate,\n rotation,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the dot product of two vectors\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec4Arg, b: Vec4Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return Math.sqrt(dx * dx + dy * dy + dz * dz + dw * dw);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return dx * dx + dy * dy + dz * dz + dw * dw;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n newDst[3] = -v[3];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec4.clone})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n newDst[3] = v[3];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec4.copy})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n newDst[3] = a[3] * b[3];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n newDst[3] = a[3] / b[3];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec4 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec4 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec4Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = v[3];\n\n newDst[0] = m[0] * x + m[4] * y + m[ 8] * z + m[12] * w;\n newDst[1] = m[1] * x + m[5] * y + m[ 9] * z + m[13] * w;\n newDst[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;\n newDst[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;\n\n return newDst;\n}\n\n\n/**\n * Treat a 4D vector as a direction and set it's length\n *\n * @param a The vec4 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec4Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec4 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec4Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n zero,\n transformMat4,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Vec4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Vec4`. In other words you can do this\n *\n * const v = vec4.cross(v1, v2); // Creates a new Vec4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec4.create();\n * vec4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. 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\ No newline at end of file diff --git a/dist/3.x/wgpu-matrix.module.js b/dist/3.x/wgpu-matrix.module.js index 8bf8de6..9ff0616 100644 --- a/dist/3.x/wgpu-matrix.module.js +++ b/dist/3.x/wgpu-matrix.module.js @@ -1,4 +1,4 @@ -/* wgpu-matrix@3.0.1, license MIT */ +/* wgpu-matrix@3.0.2, license MIT */ function wrapConstructor(OriginalConstructor, modifier) { return class extends OriginalConstructor { constructor(...args) { @@ -4678,7 +4678,7 @@ function getAPIImpl$1(Ctor) { newDst[0] = 0; newDst[1] = 0; newDst[2] = 0; - newDst[3] = 0; + newDst[3] = 1; } return newDst; } @@ -5531,6 +5531,10 @@ function getAPI(Ctor) { return api; } +/** + * Some docs + * @namespace wgpu-matrix + */ /** * Generate wgpu-matrix API for type */ @@ -5551,43 +5555,97 @@ function wgpuMatrixAPI(Mat3Ctor, Mat4Ctor, QuatCtor, Vec2Ctor, Vec3Ctor, Vec4Cto }; } const { -/** @namespace */ +/** + * 4x4 Matrix functions that default to returning `Float32Array` + * @namespace + */ mat4, -/** @namespace */ +/** + * 3x3 Matrix functions that default to returning `Float32Array` + * @namespace + */ mat3, -/** @namespace */ +/** + * Quaternion functions that default to returning `Float32Array` + * @namespace + */ quat, -/** @namespace */ +/** + * Vec2 functions that default to returning `Float32Array` + * @namespace + */ vec2, -/** @namespace */ +/** + * Vec3 functions that default to returning `Float32Array` + * @namespace + */ vec3, -/** @namespace */ +/** + * Vec3 functions that default to returning `Float32Array` + * @namespace + */ vec4, } = wgpuMatrixAPI(Float32Array, Float32Array, Float32Array, Float32Array, Float32Array, Float32Array); const { -/** @namespace */ +/** + * 4x4 Matrix functions that default to returning `Float64Array` + * @namespace + */ mat4: mat4d, -/** @namespace */ +/** + * 3x3 Matrix functions that default to returning `Float64Array` + * @namespace + */ mat3: mat3d, -/** @namespace */ +/** + * Quaternion functions that default to returning `Float64Array` + * @namespace + */ quat: quatd, -/** @namespace */ +/** + * Vec2 functions that default to returning `Float64Array` + * @namespace + */ vec2: vec2d, -/** @namespace */ +/** + * Vec3 functions that default to returning `Float64Array` + * @namespace + */ vec3: vec3d, -/** @namespace */ +/** + * Vec3 functions that default to returning `Float64Array` + * @namespace + */ vec4: vec4d, } = wgpuMatrixAPI(Float64Array, Float64Array, Float64Array, Float64Array, Float64Array, Float64Array); const { -/** @namespace */ +/** + * 4x4 Matrix functions that default to returning `number[]` + * @namespace + */ mat4: mat4n, -/** @namespace */ +/** + * 3x3 Matrix functions that default to returning `number[]` + * @namespace + */ mat3: mat3n, -/** @namespace */ +/** + * Quaternion functions that default to returning `number[]` + * @namespace + */ quat: quatn, -/** @namespace */ +/** + * Vec2 functions that default to returning `number[]` + * @namespace + */ vec2: vec2n, -/** @namespace */ +/** + * Vec3 functions that default to returning `number[]` + * @namespace + */ vec3: vec3n, -/** @namespace */ +/** + * Vec3 functions that default to returning `number[]` + * @namespace + */ vec4: vec4n, } = wgpuMatrixAPI(ZeroArray, Array, Array, Array, Array, Array); export { mat3, mat3d, mat3n, mat4, mat4d, mat4n, quat, quatd, quatn, utils, vec2, vec2d, vec2n, vec3, vec3d, vec3n, vec4, vec4d, vec4n }; diff --git a/dist/3.x/wgpu-matrix.module.js.map b/dist/3.x/wgpu-matrix.module.js.map index 2a37e66..ed75847 100644 --- a/dist/3.x/wgpu-matrix.module.js.map +++ b/dist/3.x/wgpu-matrix.module.js.map @@ -1 +1 @@ -{"version":3,"file":"wgpu-matrix.module.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/mat3-impl.ts","../../../src/vec3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n translation,\n translate,\n rotation,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the dot product of two vectors\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec4Arg, b: Vec4Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return Math.sqrt(dx * dx + dy * dy + dz * dz + dw * dw);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return dx * dx + dy * dy + dz * dz + dw * dw;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n newDst[3] = -v[3];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec4.clone})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n newDst[3] = v[3];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec4.copy})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n newDst[3] = a[3] * b[3];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n newDst[3] = a[3] / b[3];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec4 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec4 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec4Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = v[3];\n\n newDst[0] = m[0] * x + m[4] * y + m[ 8] * z + m[12] * w;\n newDst[1] = m[1] * x + m[5] * y + m[ 9] * z + m[13] * w;\n newDst[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;\n newDst[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;\n\n return newDst;\n}\n\n\n/**\n * Treat a 4D vector as a direction and set it's length\n *\n * @param a The vec4 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec4Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec4 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec4Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n zero,\n transformMat4,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Vec4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Vec4`. In other words you can do this\n *\n * const v = vec4.cross(v1, v2); // Creates a new Vec4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec4.create();\n * vec4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * vec4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: Vec4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n\n","import {BaseArgType, ZeroArray} from './types';\nimport {Mat3Arg, Mat3Type, getAPI as getMat3API} from './mat3-impl';\nimport {Mat4Arg, Mat4Type, getAPI as getMat4API} from './mat4-impl';\nimport {QuatArg, QuatType, getAPI as getQuatAPI, RotationOrder} from './quat-impl';\nimport {Vec2Arg, Vec2Type, getAPI as getVec2API} from './vec2-impl';\nimport {Vec3Arg, Vec3Type, getAPI as getVec3API} from './vec3-impl';\nimport {Vec4Arg, Vec4Type, getAPI as getVec4API} from './vec4-impl';\nimport * as utils from './utils';\n\nexport {\n RotationOrder,\n utils,\n\n BaseArgType,\n\n Mat3Arg,\n Mat4Arg,\n QuatArg,\n Vec2Arg,\n Vec3Arg,\n Vec4Arg,\n\n Mat3Type,\n Mat4Type,\n QuatType,\n Vec2Type,\n Vec3Type,\n Vec4Type,\n};\n\nexport type BaseCtor = new (n: number) => T;\n\nexport type Mat3 = Mat3Type;\nexport type Mat4 = Mat4Type;\nexport type Quat = QuatType;\nexport type Vec2 = Vec2Type;\nexport type Vec3 = Vec3Type;\nexport type Vec4 = Vec4Type;\n\nexport type Mat3d = Mat3Type;\nexport type Mat4d = Mat4Type;\nexport type Quatd = QuatType;\nexport type Vec2d = Vec2Type;\nexport type Vec3d = Vec3Type;\nexport type Vec4d = Vec4Type;\n\nexport type Mat3n = Mat3Type;\nexport type Mat4n = Mat4Type;\nexport type Quatn = QuatType;\nexport type Vec2n = Vec2Type;\nexport type Vec3n = Vec3Type;\nexport type Vec4n = Vec4Type;\n\n/**\n * Generate wgpu-matrix API for type\n */\nfunction wgpuMatrixAPI<\n Mat3 extends BaseArgType,\n Mat4 extends BaseArgType,\n Quat extends BaseArgType,\n Vec2 extends BaseArgType,\n Vec3 extends BaseArgType,\n Vec4 extends BaseArgType,\n>(\n Mat3Ctor: BaseCtor,\n Mat4Ctor: BaseCtor,\n QuatCtor: BaseCtor,\n Vec2Ctor: BaseCtor,\n Vec3Ctor: BaseCtor,\n Vec4Ctor: BaseCtor,\n) {\n return {\n /** @namespace mat4 */\n mat4: getMat4API(Mat3Ctor),\n /** @namespace mat3 */\n mat3: getMat3API(Mat4Ctor),\n /** @namespace quat */\n quat: getQuatAPI(QuatCtor),\n /** @namespace vec2 */\n vec2: getVec2API(Vec2Ctor),\n /** @namespace vec3 */\n vec3: getVec3API(Vec3Ctor),\n /** @namespace vec4 */\n vec4: getVec4API(Vec4Ctor),\n };\n}\n\nexport const {\n /** @namespace */\n mat4,\n /** @namespace */\n mat3,\n /** @namespace */\n quat,\n /** @namespace */\n vec2,\n /** @namespace */\n vec3,\n /** @namespace */\n vec4,\n} = wgpuMatrixAPI<\n Mat3, Mat4, Quat, Vec2, Vec3, Vec4>(\n Float32Array, Float32Array, Float32Array, Float32Array, Float32Array, Float32Array);\n\nexport const {\n /** @namespace */\n mat4: mat4d,\n /** @namespace */\n mat3: mat3d,\n /** @namespace */\n quat: quatd,\n /** @namespace */\n vec2: vec2d,\n /** @namespace */\n vec3: vec3d,\n /** @namespace */\n vec4: vec4d,\n} = wgpuMatrixAPI<\n Mat3d, Mat4d, Quatd, Vec2d, Vec3d, Vec4d>(\n Float64Array, Float64Array, Float64Array, Float64Array, Float64Array, Float64Array);\n\nexport const {\n /** @namespace */\n mat4: mat4n,\n /** @namespace */\n mat3: mat3n,\n /** @namespace */\n quat: quatn,\n /** @namespace */\n vec2: vec2n,\n /** @namespace */\n vec3: vec3n,\n /** @namespace */\n vec4: vec4n,\n} = wgpuMatrixAPI<\n Mat3n, Mat4n, Quatn, Vec2n, Vec3n, Vec4n>(\n ZeroArray, Array, Array, Array, Array, 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\ No newline at end of file +{"version":3,"file":"wgpu-matrix.module.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/mat3-impl.ts","../../../src/vec3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n translation,\n translate,\n rotation,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the dot product of two vectors\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec4Arg, b: Vec4Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return Math.sqrt(dx * dx + dy * dy + dz * dz + dw * dw);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return dx * dx + dy * dy + dz * dz + dw * dw;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n newDst[3] = -v[3];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec4.clone})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n newDst[3] = v[3];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec4.copy})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n newDst[3] = a[3] * b[3];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n newDst[3] = a[3] / b[3];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec4 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec4 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec4Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = v[3];\n\n newDst[0] = m[0] * x + m[4] * y + m[ 8] * z + m[12] * w;\n newDst[1] = m[1] * x + m[5] * y + m[ 9] * z + m[13] * w;\n newDst[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;\n newDst[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;\n\n return newDst;\n}\n\n\n/**\n * Treat a 4D vector as a direction and set it's length\n *\n * @param a The vec4 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec4Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec4 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec4Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n zero,\n transformMat4,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Vec4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Vec4`. In other words you can do this\n *\n * const v = vec4.cross(v1, v2); // Creates a new Vec4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec4.create();\n * vec4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * vec4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: Vec4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n\n","/**\n * Some docs\n * @namespace wgpu-matrix\n */\nimport {BaseArgType, ZeroArray} from './types';\nimport {Mat3Arg, Mat3Type, getAPI as getMat3API} from './mat3-impl';\nimport {Mat4Arg, Mat4Type, getAPI as getMat4API} from './mat4-impl';\nimport {QuatArg, QuatType, getAPI as getQuatAPI, RotationOrder} from './quat-impl';\nimport {Vec2Arg, Vec2Type, getAPI as getVec2API} from './vec2-impl';\nimport {Vec3Arg, Vec3Type, getAPI as getVec3API} from './vec3-impl';\nimport {Vec4Arg, Vec4Type, getAPI as getVec4API} from './vec4-impl';\nimport * as utils from './utils';\n\nexport {\n RotationOrder,\n utils,\n\n BaseArgType,\n\n Mat3Arg,\n Mat4Arg,\n QuatArg,\n Vec2Arg,\n Vec3Arg,\n Vec4Arg,\n\n Mat3Type,\n Mat4Type,\n QuatType,\n Vec2Type,\n Vec3Type,\n Vec4Type,\n};\n\nexport type BaseCtor = new (n: number) => T;\n\nexport type Mat3 = Mat3Type;\nexport type Mat4 = Mat4Type;\nexport type Quat = QuatType;\nexport type Vec2 = Vec2Type;\nexport type Vec3 = Vec3Type;\nexport type Vec4 = Vec4Type;\n\nexport type Mat3d = Mat3Type;\nexport type Mat4d = Mat4Type;\nexport type Quatd = QuatType;\nexport type Vec2d = Vec2Type;\nexport type Vec3d = Vec3Type;\nexport type Vec4d = Vec4Type;\n\nexport type Mat3n = Mat3Type;\nexport type Mat4n = Mat4Type;\nexport type Quatn = QuatType;\nexport type Vec2n = Vec2Type;\nexport type Vec3n = Vec3Type;\nexport type Vec4n = Vec4Type;\n\n/**\n * Generate wgpu-matrix API for type\n */\nfunction wgpuMatrixAPI<\n Mat3 extends BaseArgType,\n Mat4 extends BaseArgType,\n Quat extends BaseArgType,\n Vec2 extends BaseArgType,\n Vec3 extends BaseArgType,\n Vec4 extends BaseArgType,\n>(\n Mat3Ctor: BaseCtor,\n Mat4Ctor: BaseCtor,\n QuatCtor: BaseCtor,\n Vec2Ctor: BaseCtor,\n Vec3Ctor: BaseCtor,\n Vec4Ctor: BaseCtor,\n) {\n return {\n /** @namespace mat4 */\n mat4: getMat4API(Mat3Ctor),\n /** @namespace mat3 */\n mat3: getMat3API(Mat4Ctor),\n /** @namespace quat */\n quat: getQuatAPI(QuatCtor),\n /** @namespace vec2 */\n vec2: getVec2API(Vec2Ctor),\n /** @namespace vec3 */\n vec3: getVec3API(Vec3Ctor),\n /** @namespace vec4 */\n vec4: getVec4API(Vec4Ctor),\n };\n}\n\nexport const {\n /**\n * 4x4 Matrix functions that default to returning `Float32Array`\n * @namespace\n */\n mat4,\n /**\n * 3x3 Matrix functions that default to returning `Float32Array`\n * @namespace\n */\n mat3,\n /**\n * Quaternion functions that default to returning `Float32Array`\n * @namespace\n */\n quat,\n /**\n * Vec2 functions that default to returning `Float32Array`\n * @namespace\n */\n vec2,\n /**\n * Vec3 functions that default to returning `Float32Array`\n * @namespace\n */\n vec3,\n /**\n * Vec3 functions that default to returning `Float32Array`\n * @namespace\n */\n vec4,\n} = wgpuMatrixAPI<\n Mat3, Mat4, Quat, Vec2, Vec3, Vec4>(\n Float32Array, Float32Array, Float32Array, Float32Array, Float32Array, Float32Array);\n\nexport const {\n /**\n * 4x4 Matrix functions that default to returning `Float64Array`\n * @namespace\n */\n mat4: mat4d,\n /**\n * 3x3 Matrix functions that default to returning `Float64Array`\n * @namespace\n */\n mat3: mat3d,\n /**\n * Quaternion functions that default to returning `Float64Array`\n * @namespace\n */\n quat: quatd,\n /**\n * Vec2 functions that default to returning `Float64Array`\n * @namespace\n */\n vec2: vec2d,\n /**\n * Vec3 functions that default to returning `Float64Array`\n * @namespace\n */\n vec3: vec3d,\n /**\n * Vec3 functions that default to returning `Float64Array`\n * @namespace\n */\n vec4: vec4d,\n} = wgpuMatrixAPI<\n Mat3d, Mat4d, Quatd, Vec2d, Vec3d, Vec4d>(\n Float64Array, Float64Array, Float64Array, Float64Array, Float64Array, Float64Array);\n\nexport const {\n /**\n * 4x4 Matrix functions that default to returning `number[]`\n * @namespace\n */\n mat4: mat4n,\n /**\n * 3x3 Matrix functions that default to returning `number[]`\n * @namespace\n */\n mat3: mat3n,\n /**\n * Quaternion functions that default to returning `number[]`\n * @namespace\n */\n quat: quatn,\n /**\n * Vec2 functions that default to returning `number[]`\n * @namespace\n */\n vec2: vec2n,\n /**\n * Vec3 functions that default to returning `number[]`\n * @namespace\n */\n vec3: vec3n,\n /**\n * Vec3 functions that default to returning `number[]`\n * @namespace\n */\n vec4: vec4n,\n} = wgpuMatrixAPI<\n Mat3n, Mat4n, Quatn, Vec2n, Vec3n, Vec4n>(\n ZeroArray, Array, Array, Array, Array, 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n(4);return c[0]=t[0]+e*(r[0]-t[0]),c[1]=t[1]+e*(r[1]-t[1]),c[2]=t[2]+e*(r[2]-t[2]),c[3]=t[3]+e*(r[3]-t[3]),c},length:v,len:p,lengthSq:q,lenSq:b,normalize:g,equalsApproximately:function(n,t){return Math.abs(n[0]-t[0]).999999?(u[0]=0,u[1]=0,u[2]=0,u[3]=1,u):(t.cross(r,e,x),u[0]=x[0],u[1]=x[1],u[2]=x[2],u[3]=1+a,g(u,u))},sqlerp:function(t,r,e,o,c,u){const a=u??new n(4);return s(t,o,c,S),s(r,e,c,z),s(S,z,2*c*(1-c),a),a}}}(n),l.set(n,t)),t}const m=new Map;function d(n){let t=m.get(n);return t||(t=function(n){function t(t,r,e,o){const c=new n(4);return void 0!==t&&(c[0]=t,void 0!==r&&(c[1]=r,void 0!==e&&(c[2]=e,void 0!==o&&(c[3]=o)))),c}function r(t,r,e){const o=e??new n(4);return o[0]=t[0]-r[0],o[1]=t[1]-r[1],o[2]=t[2]-r[2],o[3]=t[3]-r[3],o}function o(t,r,e,o){const c=o??new n(4);return c[0]=t[0]+e*(r[0]-t[0]),c[1]=t[1]+e*(r[1]-t[1]),c[2]=t[2]+e*(r[2]-t[2]),c[3]=t[3]+e*(r[3]-t[3]),c}function c(t,r,e){const o=e??new n(4);return o[0]=t[0]*r,o[1]=t[1]*r,o[2]=t[2]*r,o[3]=t[3]*r,o}function u(t,r){const e=r??new n(4);return e[0]=1/t[0],e[1]=1/t[1],e[2]=1/t[2],e[3]=1/t[3],e}function a(n){const t=n[0],r=n[1],e=n[2],o=n[3];return Math.sqrt(t*t+r*r+e*e+o*o)}function s(n){const t=n[0],r=n[1],e=n[2],o=n[3];return t*t+r*r+e*e+o*o}function i(n,t){const r=n[0]-t[0],e=n[1]-t[1],o=n[2]-t[2],c=n[3]-t[3];return Math.sqrt(r*r+e*e+o*o+c*c)}function f(n,t){const r=n[0]-t[0],e=n[1]-t[1],o=n[2]-t[2],c=n[3]-t[3];return r*r+e*e+o*o+c*c}function M(t,r){const e=r??new n(4),o=t[0],c=t[1],u=t[2],a=t[3],s=Math.sqrt(o*o+c*c+u*u+a*a);return s>1e-5?(e[0]=o/s,e[1]=c/s,e[2]=u/s,e[3]=a/s):(e[0]=0,e[1]=0,e[2]=0,e[3]=0),e}function h(t,r){const e=r??new n(4);return e[0]=t[0],e[1]=t[1],e[2]=t[2],e[3]=t[3],e}function l(t,r,e){const o=e??new n(4);return o[0]=t[0]*r[0],o[1]=t[1]*r[1],o[2]=t[2]*r[2],o[3]=t[3]*r[3],o}function w(t,r,e){const o=e??new n(4);return o[0]=t[0]/r[0],o[1]=t[1]/r[1],o[2]=t[2]/r[2],o[3]=t[3]/r[3],o}function m(t,r,e){const o=e??new n(4);return M(t,o),c(o,r,o)}return{create:t,fromValues:t,set:function(t,r,e,o,c){const u=c??new n(4);return u[0]=t,u[1]=r,u[2]=e,u[3]=o,u},ceil:function(t,r){const e=r??new n(4);return e[0]=Math.ceil(t[0]),e[1]=Math.ceil(t[1]),e[2]=Math.ceil(t[2]),e[3]=Math.ceil(t[3]),e},floor:function(t,r){const e=r??new n(4);return e[0]=Math.floor(t[0]),e[1]=Math.floor(t[1]),e[2]=Math.floor(t[2]),e[3]=Math.floor(t[3]),e},round:function(t,r){const e=r??new n(4);return e[0]=Math.round(t[0]),e[1]=Math.round(t[1]),e[2]=Math.round(t[2]),e[3]=Math.round(t[3]),e},clamp:function(t,r=0,e=1,o){const c=o??new n(4);return c[0]=Math.min(e,Math.max(r,t[0])),c[1]=Math.min(e,Math.max(r,t[1])),c[2]=Math.min(e,Math.max(r,t[2])),c[3]=Math.min(e,Math.max(r,t[3])),c},add:function(t,r,e){const o=e??new n(4);return o[0]=t[0]+r[0],o[1]=t[1]+r[1],o[2]=t[2]+r[2],o[3]=t[3]+r[3],o},addScaled:function(t,r,e,o){const c=o??new n(4);return c[0]=t[0]+r[0]*e,c[1]=t[1]+r[1]*e,c[2]=t[2]+r[2]*e,c[3]=t[3]+r[3]*e,c},subtract:r,sub:r,equalsApproximately:function(n,t){return Math.abs(n[0]-t[0])r?m(t,r,o):h(t,o)},midpoint:function(t,r,e){return o(t,r,.5,e??new n(4))}}}(n),m.set(n,t)),t}function v(n,t,r,e,o,c){return{mat4:h(n),mat3:s(t),quat:w(r),vec2:u(e),vec3:f(o),vec4:d(c)}}const{mat4:p,mat3:q,quat:b,vec2:g,vec3:x,vec4:y}=v(Float32Array,Float32Array,Float32Array,Float32Array,Float32Array,Float32Array),{mat4:A,mat3:S,quat:z,vec2:F,vec3:k,vec4:T}=v(Float64Array,Float64Array,Float64Array,Float64Array,Float64Array,Float64Array),{mat4:I,mat3:P,quat:V,vec2:Z,vec3:L,vec4:R}=v(n,Array,Array,Array,Array,Array);export{q as mat3,S as mat3d,P as mat3n,p as mat4,A as mat4d,I as mat4n,b as quat,z as quatd,V as quatn,o as utils,g as vec2,F as vec2d,Z as vec2n,x as vec3,k as vec3d,L as vec3n,y as vec4,T as vec4d,R as vec4n}; //# sourceMappingURL=wgpu-matrix.module.min.js.map diff --git a/dist/3.x/wgpu-matrix.module.min.js.map b/dist/3.x/wgpu-matrix.module.min.js.map index 39e55e2..ab24ad0 100644 --- a/dist/3.x/wgpu-matrix.module.min.js.map +++ b/dist/3.x/wgpu-matrix.module.min.js.map @@ -1 +1 @@ -{"version":3,"file":"wgpu-matrix.module.min.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/mat3-impl.ts","../../../src/vec3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n translation,\n translate,\n rotation,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. 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If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n newDst[3] = a[3] / b[3];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. 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\ No newline at end of file +{"version":3,"file":"wgpu-matrix.module.min.js","sources":["../../../src/types.ts","../../../src/utils.ts","../../../src/vec2-impl.ts","../../../src/mat3-impl.ts","../../../src/vec3-impl.ts","../../../src/mat4-impl.ts","../../../src/quat-impl.ts","../../../src/vec4-impl.ts","../../../src/wgpu-matrix.ts"],"sourcesContent":["/**\n * The types you can pass to most functions that take an\n * array of numbers.\n */\nexport type BaseArgType = Float32Array | Float64Array | number[];\n\nfunction wrapConstructor any>(\n OriginalConstructor: T,\n modifier: (instance: InstanceType) => void\n): T {\n return class extends OriginalConstructor {\n constructor(...args: any[]) {\n super(...args);\n modifier(this as InstanceType);\n }\n } as T; // Type assertion is necessary here\n}\n\nexport const ZeroArray = wrapConstructor(Array, a => a.fill(0));\n\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nexport let EPSILON = 0.000001;\n\n/**\n * Set the value for EPSILON for various checks\n * @param v - Value to use for EPSILON.\n * @returns previous value of EPSILON;\n */\nexport function setEpsilon(v: number): number {\n const old = EPSILON;\n EPSILON = v;\n return old;\n}\n\n/**\n * Convert degrees to radians\n * @param degrees - Angle in degrees\n * @returns angle converted to radians\n */\nexport function degToRad(degrees: number): number {\n return degrees * Math.PI / 180;\n}\n\n/**\n * Convert radians to degrees\n * @param radians - Angle in radians\n * @returns angle converted to degrees\n */\nexport function radToDeg(radians: number): number {\n return radians * 180 / Math.PI;\n}\n\n/**\n * Lerps between a and b via t\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @returns a + (b - a) * t\n */\nexport function lerp(a: number, b: number, t: number): number {\n return a + (b - a) * t;\n}\n\n/**\n * Compute the opposite of lerp. Given a and b and a value between\n * a and b returns a value between 0 and 1. 0 if a, 1 if b.\n * Note: no clamping is done.\n * @param a - start value\n * @param b - end value\n * @param v - value between a and b\n * @returns (v - a) / (b - a)\n */\nexport function inverseLerp(a: number, b: number, v: number): number {\n const d = b - a;\n return (Math.abs(b - a) < EPSILON)\n ? a\n : (v - a) / d;\n}\n\n/**\n * Compute the euclidean modulo\n *\n * ```\n * // table for n / 3\n * -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 <- n\n * ------------------------------------\n * -2 -1 -0 -2 -1 0, 1, 2, 0, 1, 2 <- n % 3\n * 1 2 0 1 2 0, 1, 2, 0, 1, 2 <- euclideanModule(n, 3)\n * ```\n *\n * @param n - dividend\n * @param m - divisor\n * @returns the euclidean modulo of n / m\n */\nexport function euclideanModulo(n: number, m: number) {\n return ((n % m) + m) % m;\n}","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg, Vec2Type } from './vec2';\nimport { Vec3Arg } from './vec3';\nimport { BaseArgType } from './types';\n\nexport { Vec2Arg, Vec2Type };\n\ntype Vec2Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n */\nfunction getAPIImpl(Ctor: Vec2Ctor) {\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values.\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Vec2's specified type\n * it would be faster to use\n *\n * ```\n * const v = vec2.clone(someJSArray);\n * ```\n *\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nfunction create(x = 0, y = 0) {\n const newDst = new Ctor(2);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Vec2; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec2\n * Also see {@link vec2.create} and {@link vec2.copy}\n *\n * @param x first value\n * @param y second value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec2Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec2Arg, b: Vec2Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec2Arg, b: Vec2Arg): number {\n const ax = a[0];\n const ay = a[1];\n const bx = b[0];\n const by = b[1];\n const mag1 = Math.sqrt(ax * ax + ay * ay);\n const mag2 = Math.sqrt(bx * bx + by * by);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec2Arg, b: Vec2Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec2Arg, b: Vec2Arg): boolean {\n return a[0] === b[0] && a[1] === b[1];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec2Arg, b: Vec2Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec2Arg, b: Vec2Arg, t: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec2Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const z = a[0] * b[1] - a[1] * b[0];\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec2Arg, b: Vec2Arg): number {\n return a[0] * b[0] + a[1] * b[1];\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return Math.sqrt(v0 * v0 + v1 * v1);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec2Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n return v0 * v0 + v1 * v1;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return Math.sqrt(dx * dx + dy * dy);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec2Arg, b: Vec2Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n return dx * dx + dy * dy;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const len = Math.sqrt(v0 * v0 + v1 * v1);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec2.clone})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec2.copy})\n * Also see {@link vec2.create} and {@link vec2.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random unit vector * scale\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n newDst[0] = Math.cos(angle) * scale;\n newDst[1] = Math.sin(angle) * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform Vec2 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec2Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = x * m[0] + y * m[4] + m[12];\n newDst[1] = x * m[1] + y * m[5] + m[13];\n\n return newDst;\n}\n\n/**\n * Transforms vec4 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional Vec2 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec2Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n const x = v[0];\n const y = v[1];\n\n newDst[0] = m[0] * x + m[4] * y + m[8];\n newDst[1] = m[1] * x + m[5] * y + m[9];\n\n return newDst;\n}\n\n/**\n * Rotate a 2D vector\n *\n * @param a The vec2 point to rotate\n * @param b The origin of the rotation\n * @param rad The angle of rotation in radians\n * @returns the rotated vector\n */\nfunction rotate(a: Vec2Arg, b: Vec2Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n // Translate point to the origin\n const p0 = a[0] - b[0];\n const p1 = a[1] - b[1];\n const sinC = Math.sin(rad);\n const cosC = Math.cos(rad);\n\n //perform rotation and translate to correct position\n newDst[0] = p0 * cosC - p1 * sinC + b[0];\n newDst[1] = p0 * sinC + p1 * cosC + b[1];\n\n return newDst;\n}\n\n/**\n * Treat a 2D vector as a direction and set it's length\n *\n * @param a The vec2 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec2Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec2 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec2Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec2Arg, b: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(2)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat3,\n rotate,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec2Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\n\nimport * as utils from './utils.js';\nimport { QuatArg } from './quat';\nimport { Mat3Arg, Mat3Type } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { Vec2Arg } from './vec2';\nimport { getAPI as getVec2API } from './vec2-impl';\nimport { BaseArgType } from './types';\n\nexport { Mat3Arg, Mat3Type };\n\ntype Mat3Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat3\n * */\nfunction getAPIImpl(Ctor: Mat3Ctor) {\n const vec2 = getVec2API(Ctor);\n\n/**\n * Create a Mat3 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat3's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat3.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @returns matrix created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number,\n v3?: number, v4?: number, v5?: number,\n v6?: number, v7?: number, v8?: number) {\n const newDst = new Ctor(12);\n // to make the array homogenous\n newDst[3] = 0;\n newDst[7] = 0;\n newDst[11] = 0;\n\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[4] = v3;\n if (v4 !== undefined) {\n newDst[5] = v4;\n if (v5 !== undefined) {\n newDst[6] = v5;\n if (v6 !== undefined) {\n newDst[8] = v6;\n if (v7 !== undefined) {\n newDst[9] = v7;\n if (v8 !== undefined) {\n newDst[10] = v8;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n\n return newDst;\n}\n\n/**\n * Sets the values of a Mat3\n * Also see {@link mat3.create} and {@link mat3.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 set from values.\n */\nfunction set(\n v0: number, v1: number, v2: number,\n v3: number, v4: number, v5: number,\n v6: number, v7: number, v8: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[0] = v0; newDst[1] = v1; newDst[ 2] = v2; newDst[ 3] = 0;\n newDst[4] = v3; newDst[5] = v4; newDst[ 6] = v5; newDst[ 7] = 0;\n newDst[8] = v6; newDst[9] = v7; newDst[10] = v8; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Creates a Mat3 from the upper left 3x3 part of a Mat4\n * @param m4 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from m4\n */\nfunction fromMat4(m4: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n newDst[0] = m4[0]; newDst[1] = m4[1]; newDst[ 2] = m4[ 2]; newDst[ 3] = 0;\n newDst[4] = m4[4]; newDst[5] = m4[5]; newDst[ 6] = m4[ 6]; newDst[ 7] = 0;\n newDst[8] = m4[8]; newDst[9] = m4[9]; newDst[10] = m4[10]; newDst[11] = 0;\n return newDst;\n}\n\n/**\n * Creates a Mat3 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat3 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat3.clone})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat3.copy})\n * Also see {@link mat3.create} and {@link mat3.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat3Arg, b: Mat3Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a Operand matrix.\n * @param b Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat3Arg, b: Mat3Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10];\n}\n\n/**\n * Creates a 3-by-3 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 3-by-3 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n if (newDst === m) {\n let t: number;\n\n // 0 1 2\n // 4 5 6\n // 8 9 10\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n const b01 = m22 * m11 - m12 * m21;\n const b11 = -m22 * m10 + m12 * m20;\n const b21 = m21 * m10 - m11 * m20;\n\n const invDet = 1 / (m00 * b01 + m01 * b11 + m02 * b21);\n\n newDst[ 0] = b01 * invDet;\n newDst[ 1] = (-m22 * m01 + m02 * m21) * invDet;\n newDst[ 2] = ( m12 * m01 - m02 * m11) * invDet;\n newDst[ 4] = b11 * invDet;\n newDst[ 5] = ( m22 * m00 - m02 * m20) * invDet;\n newDst[ 6] = (-m12 * m00 + m02 * m10) * invDet;\n newDst[ 8] = b21 * invDet;\n newDst[ 9] = (-m21 * m00 + m01 * m20) * invDet;\n newDst[10] = ( m11 * m00 - m01 * m10) * invDet;\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat3Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n return m00 * (m11 * m22 - m21 * m12) -\n m10 * (m01 * m22 - m21 * m02) +\n m20 * (m01 * m12 - m11 * m02);\n}\n\n/**\n * Computes the inverse of a 3-by-3 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat3Arg, b: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22;\n\n return newDst;\n}\n\n/**\n * Multiplies two 3-by-3 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 3-by-3 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n }\n newDst[ 8] = v[0];\n newDst[ 9] = v[1];\n newDst[10] = 1;\n return newDst;\n}\n\n/**\n * Returns the translation component of a 3-by-3 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n newDst[0] = m[8];\n newDst[1] = m[9];\n return newDst;\n}\n\n/**\n * Returns an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y,\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat3Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec2.create()) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n return newDst;\n}\n\n/**\n * Sets an axis of a 3x3 matrix as a vector with 2 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat3Arg, v: Vec2Arg, axis: number, dst?: T) {\n const newDst = (dst === m ? m : copy(m, dst)) as T;\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? vec2.create());\n\n const xx = m[0];\n const xy = m[1];\n const yx = m[4];\n const yy = m[5];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy);\n newDst[1] = Math.sqrt(yx * yx + yy * yy);\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which translates by the given vector v.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0;\n newDst[ 8] = v[0]; newDst[ 9] = v[1]; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 3-by-3 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n }\n\n newDst[ 8] = m00 * v0 + m10 * v1 + m20;\n newDst[ 9] = m01 * v0 + m11 * v1 + m21;\n newDst[10] = m02 * v0 + m12 * v1 + m22;\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which rotates by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotation(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 3-by-3 matrix by the given angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotate(m: Mat3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * 2 entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of 2 entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat3Arg, v: Vec2Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 3-by-3 matrix which scales uniformly in each dimension\n * @param s - Amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 3-by-3 matrix in each dimension by an amount\n * given.\n * @param m - The matrix to be modified.\n * @param s - Amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat3Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(12)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n }\n\n return newDst;\n}\n\nreturn {\n clone,\n create,\n set,\n fromMat4,\n fromQuat,\n negate,\n copy,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n invert,\n determinant,\n mul,\n multiply,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n translation,\n translate,\n rotation,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec3Arg, Vec3Type } from './vec3';\nimport { Mat3Arg } from './mat3';\nimport { Mat4Arg } from './mat4';\nimport { QuatArg } from './quat';\nimport { BaseArgType } from './types';\n\nexport { Vec3Arg, Vec3Type };\n\ntype Vec3Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec3\n * */\nfunction getAPIImpl(Ctor: Vec3Ctor) {\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number) {\n const newDst = new Ctor(3);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec3; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec3\n * Also see {@link vec3.create} and {@link vec3.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec3Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec3Arg, b: Vec3Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n\n return newDst;\n}\n\n/**\n * Returns the angle in radians between two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns The angle in radians between the 2 vectors.\n */\nfunction angle(a: Vec3Arg, b: Vec3Arg): number {\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const mag1 = Math.sqrt(ax * ax + ay * ay + az * az);\n const mag2 = Math.sqrt(bx * bx + by * by + bz * bz);\n const mag = mag1 * mag2;\n const cosine = mag && dot(a, b) / mag;\n return Math.acos(cosine);\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec3Arg, b: Vec3Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec3Arg, b: Vec3Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec3Arg, b: Vec3Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec3Arg, b: Vec3Arg, t: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec3Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the cross product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of a cross b.\n */\nfunction cross(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const t1 = a[2] * b[0] - a[0] * b[2];\n const t2 = a[0] * b[1] - a[1] * b[0];\n newDst[0] = a[1] * b[2] - a[2] * b[1];\n newDst[1] = t1;\n newDst[2] = t2;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two vectors; assumes both vectors have\n * three entries.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec3Arg, b: Vec3Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec3Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n return v0 * v0 + v1 * v1 + v2 * v2;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return Math.sqrt(dx * dx + dy * dy + dz * dz);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec3Arg, b: Vec3Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n return dx * dx + dy * dy + dz * dz;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec3.clone})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec3.copy})\n * Also see {@link vec3.create} and {@link vec3.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Creates a random vector\n * @param scale - Default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The random vector.\n */\nfunction random(scale = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const angle = Math.random() * 2 * Math.PI;\n const z = Math.random() * 2 - 1;\n const zScale = Math.sqrt(1 - z * z) * scale;\n newDst[0] = Math.cos(angle) * zScale;\n newDst[1] = Math.sin(angle) * zScale;\n newDst[2] = z * scale;\n\n return newDst;\n}\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec3 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = (m[3] * x + m[7] * y + m[11] * z + m[15]) || 1;\n\n newDst[0] = (m[0] * x + m[4] * y + m[8] * z + m[12]) / w;\n newDst[1] = (m[1] * x + m[5] * y + m[9] * z + m[13]) / w;\n newDst[2] = (m[2] * x + m[6] * y + m[10] * z + m[14]) / w;\n\n return newDst;\n}\n\n/**\n * Transform vec3 by upper 3x3 matrix inside 4x4 matrix.\n * @param v - The direction.\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns The transformed vector.\n */\nfunction transformMat4Upper3x3(v: Vec3Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[0] = v0 * m[0 * 4 + 0] + v1 * m[1 * 4 + 0] + v2 * m[2 * 4 + 0];\n newDst[1] = v0 * m[0 * 4 + 1] + v1 * m[1 * 4 + 1] + v2 * m[2 * 4 + 1];\n newDst[2] = v0 * m[0 * 4 + 2] + v1 * m[1 * 4 + 2] + v2 * m[2 * 4 + 2];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by 3x3 matrix\n *\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat3(v: Vec3Arg, m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n newDst[0] = x * m[0] + y * m[4] + z * m[8];\n newDst[1] = x * m[1] + y * m[5] + z * m[9];\n newDst[2] = x * m[2] + y * m[6] + z * m[10];\n\n return newDst;\n}\n\n/**\n * Transforms vec3 by Quaternion\n * @param v - the vector to transform\n * @param q - the quaternion to transform by\n * @param dst - optional vec3 to store result. If not passed a new one is created.\n * @returns the transformed\n */\nfunction transformQuat(v: Vec3Arg, q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const w2 = q[3] * 2;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n\n const uvX = qy * z - qz * y;\n const uvY = qz * x - qx * z;\n const uvZ = qx * y - qy * x;\n\n newDst[0] = x + uvX * w2 + (qy * uvZ - qz * uvY) * 2;\n newDst[1] = y + uvY * w2 + (qz * uvX - qx * uvZ) * 2;\n newDst[2] = z + uvZ * w2 + (qx * uvY - qy * uvX) * 2;\n\n return newDst;\n}\n\n/**\n * Returns the translation component of a 4-by-4 matrix as a vector with 3\n * entries.\n * @param m - The matrix.\n * @param dst - vector to hold result. If not passed a new one is created.\n * @returns The translation component of m.\n */\nfunction getTranslation(m: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n/**\n * Returns the scaling component of the matrix\n * @param m - The Matrix\n * @param dst - The vector to set. If not passed a new one is created.\n */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the x-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateX(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n //Translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n //perform rotation\n r[0] = p[0];\n r[1] = p[1] * Math.cos(rad) - p[2] * Math.sin(rad);\n r[2] = p[1] * Math.sin(rad) + p[2] * Math.cos(rad);\n\n //translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the y-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns the rotated vector\n */\nfunction rotateY(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[2] * Math.sin(rad) + p[0] * Math.cos(rad);\n r[1] = p[1];\n r[2] = p[2] * Math.cos(rad) - p[0] * Math.sin(rad);\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Rotate a 3D vector around the z-axis\n *\n * @param {ReadonlyVec3} a The vec3 point to rotate\n * @param {ReadonlyVec3} b The origin of the rotation\n * @param {Number} rad The angle of rotation in radians\n * @param dst - The vector to set. If not passed a new one is created.\n * @returns {vec3} out\n */\nfunction rotateZ(a: Vec3Arg, b: Vec3Arg, rad: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n const p = [];\n const r = [];\n\n // translate point to the origin\n p[0] = a[0] - b[0];\n p[1] = a[1] - b[1];\n p[2] = a[2] - b[2];\n\n // perform rotation\n r[0] = p[0] * Math.cos(rad) - p[1] * Math.sin(rad);\n r[1] = p[0] * Math.sin(rad) + p[1] * Math.cos(rad);\n r[2] = p[2];\n\n // translate to correct position\n newDst[0] = r[0] + b[0];\n newDst[1] = r[1] + b[1];\n newDst[2] = r[2] + b[2];\n\n return newDst;\n}\n\n/**\n * Treat a 3D vector as a direction and set it's length\n *\n * @param a The vec3 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec3Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec3 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec3Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec3Arg, b: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(3)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n angle,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n cross,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n random,\n zero,\n transformMat4,\n transformMat4Upper3x3,\n transformMat3,\n transformQuat,\n getTranslation,\n getAxis,\n getScaling,\n rotateX,\n rotateY,\n rotateZ,\n setLength,\n truncate,\n midpoint,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Vec3Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","import { Mat4Arg, Mat4Type } from './mat4';\nimport { Mat3Arg } from './mat3';\nimport { QuatArg } from './quat';\nimport { Vec3Arg } from './vec3';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\nimport * as utils from './utils';\n\nexport { Mat4Arg, Mat4Type };\n\ntype Mat4Ctor = new (n: number) => T;\n\n/**\n * Generates a typed API for Mat4\n * */\nfunction getAPIImpl(Ctor: Mat4Ctor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * 4x4 Matrix math math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new matrix. In other words you can do this\n *\n * const mat = mat4.translation([1, 2, 3]); // Creates a new translation matrix\n *\n * or\n *\n * const mat = mat4.create();\n * mat4.translation([1, 2, 3], mat); // Puts translation matrix in mat.\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always save to pass any matrix as the destination. So for example\n *\n * const mat = mat4.identity();\n * const trans = mat4.translation([1, 2, 3]);\n * mat4.multiply(mat, trans, mat); // Multiplies mat * trans and puts result in mat.\n *\n */\n\n\n/**\n * Create a Mat4 from values\n *\n * Note: Since passing in a raw JavaScript array\n * is valid in all circumstances, if you want to\n * force a JavaScript array into a Mat4's specified type\n * it would be faster to use\n *\n * ```\n * const m = mat4.clone(someJSArray);\n * ```\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @returns created from values.\n */\nfunction create(\n v0?: number, v1?: number, v2?: number, v3?: number,\n v4?: number, v5?: number, v6?: number, v7?: number,\n v8?: number, v9?: number, v10?: number, v11?: number,\n v12?: number, v13?: number, v14?: number, v15?: number) {\n const newDst = new Ctor(16);\n if (v0 !== undefined) {\n newDst[0] = v0;\n if (v1 !== undefined) {\n newDst[1] = v1;\n if (v2 !== undefined) {\n newDst[2] = v2;\n if (v3 !== undefined) {\n newDst[3] = v3;\n if (v4 !== undefined) {\n newDst[4] = v4;\n if (v5 !== undefined) {\n newDst[5] = v5;\n if (v6 !== undefined) {\n newDst[6] = v6;\n if (v7 !== undefined) {\n newDst[7] = v7;\n if (v8 !== undefined) {\n newDst[8] = v8;\n if (v9 !== undefined) {\n newDst[9] = v9;\n if (v10 !== undefined) {\n newDst[10] = v10;\n if (v11 !== undefined) {\n newDst[11] = v11;\n if (v12 !== undefined) {\n newDst[12] = v12;\n if (v13 !== undefined) {\n newDst[13] = v13;\n if (v14 !== undefined) {\n newDst[14] = v14;\n if (v15 !== undefined) {\n newDst[15] = v15;\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Sets the values of a Mat4\n * Also see {@link mat4.create} and {@link mat4.copy}\n *\n * @param v0 - value for element 0\n * @param v1 - value for element 1\n * @param v2 - value for element 2\n * @param v3 - value for element 3\n * @param v4 - value for element 4\n * @param v5 - value for element 5\n * @param v6 - value for element 6\n * @param v7 - value for element 7\n * @param v8 - value for element 8\n * @param v9 - value for element 9\n * @param v10 - value for element 10\n * @param v11 - value for element 11\n * @param v12 - value for element 12\n * @param v13 - value for element 13\n * @param v14 - value for element 14\n * @param v15 - value for element 15\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 created from values.\n */\nfunction set(\n v0: number, v1: number, v2: number, v3: number,\n v4: number, v5: number, v6: number, v7: number,\n v8: number, v9: number, v10: number, v11: number,\n v12: number, v13: number, v14: number, v15: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v0; newDst[ 1] = v1; newDst[ 2] = v2; newDst[ 3] = v3;\n newDst[ 4] = v4; newDst[ 5] = v5; newDst[ 6] = v6; newDst[ 7] = v7;\n newDst[ 8] = v8; newDst[ 9] = v9; newDst[10] = v10; newDst[11] = v11;\n newDst[12] = v12; newDst[13] = v13; newDst[14] = v14; newDst[15] = v15;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 from a Mat3\n * @param m3 - source matrix\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from m3\n */\nfunction fromMat3(m3: Mat3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m3[0]; newDst[ 1] = m3[1]; newDst[ 2] = m3[ 2]; newDst[ 3] = 0;\n newDst[ 4] = m3[4]; newDst[ 5] = m3[5]; newDst[ 6] = m3[ 6]; newDst[ 7] = 0;\n newDst[ 8] = m3[8]; newDst[ 9] = m3[9]; newDst[10] = m3[10]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a Mat4 rotation matrix from a quaternion\n * @param q - quaternion to create matrix from\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns Mat4 made from q\n */\nfunction fromQuat(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const x = q[0]; const y = q[1]; const z = q[2]; const w = q[3];\n const x2 = x + x; const y2 = y + y; const z2 = z + z;\n\n const xx = x * x2;\n const yx = y * x2;\n const yy = y * y2;\n const zx = z * x2;\n const zy = z * y2;\n const zz = z * z2;\n const wx = w * x2;\n const wy = w * y2;\n const wz = w * z2;\n\n newDst[ 0] = 1 - yy - zz; newDst[ 1] = yx + wz; newDst[ 2] = zx - wy; newDst[ 3] = 0;\n newDst[ 4] = yx - wz; newDst[ 5] = 1 - xx - zz; newDst[ 6] = zy + wx; newDst[ 7] = 0;\n newDst[ 8] = zx + wy; newDst[ 9] = zy - wx; newDst[10] = 1 - xx - yy; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Negates a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns -m.\n */\nfunction negate(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = -m[ 0]; newDst[ 1] = -m[ 1]; newDst[ 2] = -m[ 2]; newDst[ 3] = -m[ 3];\n newDst[ 4] = -m[ 4]; newDst[ 5] = -m[ 5]; newDst[ 6] = -m[ 6]; newDst[ 7] = -m[ 7];\n newDst[ 8] = -m[ 8]; newDst[ 9] = -m[ 9]; newDst[10] = -m[10]; newDst[11] = -m[11];\n newDst[12] = -m[12]; newDst[13] = -m[13]; newDst[14] = -m[14]; newDst[15] = -m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix. (same as {@link mat4.clone})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nfunction copy(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = m[ 0]; newDst[ 1] = m[ 1]; newDst[ 2] = m[ 2]; newDst[ 3] = m[ 3];\n newDst[ 4] = m[ 4]; newDst[ 5] = m[ 5]; newDst[ 6] = m[ 6]; newDst[ 7] = m[ 7];\n newDst[ 8] = m[ 8]; newDst[ 9] = m[ 9]; newDst[10] = m[10]; newDst[11] = m[11];\n newDst[12] = m[12]; newDst[13] = m[13]; newDst[14] = m[14]; newDst[15] = m[15];\n\n return newDst;\n}\n\n/**\n * Copies a matrix (same as {@link mat4.copy})\n * Also see {@link mat4.create} and {@link mat4.set}\n * @param m - The matrix.\n * @param dst - The matrix. If not passed a new one is created.\n * @returns A copy of m.\n */\nconst clone = copy;\n\n/**\n * Check if 2 matrices are approximately equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are approximately equal\n */\nfunction equalsApproximately(a: Mat4Arg, b: Mat4Arg): boolean {\n return Math.abs(a[ 0] - b[ 0]) < utils.EPSILON &&\n Math.abs(a[ 1] - b[ 1]) < utils.EPSILON &&\n Math.abs(a[ 2] - b[ 2]) < utils.EPSILON &&\n Math.abs(a[ 3] - b[ 3]) < utils.EPSILON &&\n Math.abs(a[ 4] - b[ 4]) < utils.EPSILON &&\n Math.abs(a[ 5] - b[ 5]) < utils.EPSILON &&\n Math.abs(a[ 6] - b[ 6]) < utils.EPSILON &&\n Math.abs(a[ 7] - b[ 7]) < utils.EPSILON &&\n Math.abs(a[ 8] - b[ 8]) < utils.EPSILON &&\n Math.abs(a[ 9] - b[ 9]) < utils.EPSILON &&\n Math.abs(a[10] - b[10]) < utils.EPSILON &&\n Math.abs(a[11] - b[11]) < utils.EPSILON &&\n Math.abs(a[12] - b[12]) < utils.EPSILON &&\n Math.abs(a[13] - b[13]) < utils.EPSILON &&\n Math.abs(a[14] - b[14]) < utils.EPSILON &&\n Math.abs(a[15] - b[15]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 matrices are exactly equal\n * @param a - Operand matrix.\n * @param b - Operand matrix.\n * @returns true if matrices are exactly equal\n */\nfunction equals(a: Mat4Arg, b: Mat4Arg): boolean {\n return a[ 0] === b[ 0] &&\n a[ 1] === b[ 1] &&\n a[ 2] === b[ 2] &&\n a[ 3] === b[ 3] &&\n a[ 4] === b[ 4] &&\n a[ 5] === b[ 5] &&\n a[ 6] === b[ 6] &&\n a[ 7] === b[ 7] &&\n a[ 8] === b[ 8] &&\n a[ 9] === b[ 9] &&\n a[10] === b[10] &&\n a[11] === b[11] &&\n a[12] === b[12] &&\n a[13] === b[13] &&\n a[14] === b[14] &&\n a[15] === b[15];\n}\n\n/**\n * Creates a 4-by-4 identity matrix.\n *\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A 4-by-4 identity matrix.\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Takes the transpose of a matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The transpose of m.\n */\nfunction transpose(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n if (newDst === m) {\n let t;\n\n t = m[1];\n m[1] = m[4];\n m[4] = t;\n\n t = m[2];\n m[2] = m[8];\n m[8] = t;\n\n t = m[3];\n m[3] = m[12];\n m[12] = t;\n\n t = m[6];\n m[6] = m[9];\n m[9] = t;\n\n t = m[7];\n m[7] = m[13];\n m[13] = t;\n\n t = m[11];\n m[11] = m[14];\n m[14] = t;\n return newDst;\n }\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n newDst[ 0] = m00; newDst[ 1] = m10; newDst[ 2] = m20; newDst[ 3] = m30;\n newDst[ 4] = m01; newDst[ 5] = m11; newDst[ 6] = m21; newDst[ 7] = m31;\n newDst[ 8] = m02; newDst[ 9] = m12; newDst[10] = m22; newDst[11] = m32;\n newDst[12] = m03; newDst[13] = m13; newDst[14] = m23; newDst[15] = m33;\n\n return newDst;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix.\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nfunction inverse(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n const tmp12 = m20 * m31;\n const tmp13 = m30 * m21;\n const tmp14 = m10 * m31;\n const tmp15 = m30 * m11;\n const tmp16 = m10 * m21;\n const tmp17 = m20 * m11;\n const tmp18 = m00 * m31;\n const tmp19 = m30 * m01;\n const tmp20 = m00 * m21;\n const tmp21 = m20 * m01;\n const tmp22 = m00 * m11;\n const tmp23 = m10 * m01;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n const d = 1 / (m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3);\n\n newDst[ 0] = d * t0;\n newDst[ 1] = d * t1;\n newDst[ 2] = d * t2;\n newDst[ 3] = d * t3;\n newDst[ 4] = d * ((tmp1 * m10 + tmp2 * m20 + tmp5 * m30) -\n (tmp0 * m10 + tmp3 * m20 + tmp4 * m30));\n newDst[ 5] = d * ((tmp0 * m00 + tmp7 * m20 + tmp8 * m30) -\n (tmp1 * m00 + tmp6 * m20 + tmp9 * m30));\n newDst[ 6] = d * ((tmp3 * m00 + tmp6 * m10 + tmp11 * m30) -\n (tmp2 * m00 + tmp7 * m10 + tmp10 * m30));\n newDst[ 7] = d * ((tmp4 * m00 + tmp9 * m10 + tmp10 * m20) -\n (tmp5 * m00 + tmp8 * m10 + tmp11 * m20));\n newDst[ 8] = d * ((tmp12 * m13 + tmp15 * m23 + tmp16 * m33) -\n (tmp13 * m13 + tmp14 * m23 + tmp17 * m33));\n newDst[ 9] = d * ((tmp13 * m03 + tmp18 * m23 + tmp21 * m33) -\n (tmp12 * m03 + tmp19 * m23 + tmp20 * m33));\n newDst[10] = d * ((tmp14 * m03 + tmp19 * m13 + tmp22 * m33) -\n (tmp15 * m03 + tmp18 * m13 + tmp23 * m33));\n newDst[11] = d * ((tmp17 * m03 + tmp20 * m13 + tmp23 * m23) -\n (tmp16 * m03 + tmp21 * m13 + tmp22 * m23));\n newDst[12] = d * ((tmp14 * m22 + tmp17 * m32 + tmp13 * m12) -\n (tmp16 * m32 + tmp12 * m12 + tmp15 * m22));\n newDst[13] = d * ((tmp20 * m32 + tmp12 * m02 + tmp19 * m22) -\n (tmp18 * m22 + tmp21 * m32 + tmp13 * m02));\n newDst[14] = d * ((tmp18 * m12 + tmp23 * m32 + tmp15 * m02) -\n (tmp22 * m32 + tmp14 * m02 + tmp19 * m12));\n newDst[15] = d * ((tmp22 * m22 + tmp16 * m02 + tmp21 * m12) -\n (tmp20 * m12 + tmp23 * m22 + tmp17 * m02));\n\n return newDst;\n}\n\n/**\n * Compute the determinant of a matrix\n * @param m - the matrix\n * @returns the determinant\n */\nfunction determinant(m: Mat4Arg): number {\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n const tmp0 = m22 * m33;\n const tmp1 = m32 * m23;\n const tmp2 = m12 * m33;\n const tmp3 = m32 * m13;\n const tmp4 = m12 * m23;\n const tmp5 = m22 * m13;\n const tmp6 = m02 * m33;\n const tmp7 = m32 * m03;\n const tmp8 = m02 * m23;\n const tmp9 = m22 * m03;\n const tmp10 = m02 * m13;\n const tmp11 = m12 * m03;\n\n const t0 = (tmp0 * m11 + tmp3 * m21 + tmp4 * m31) -\n (tmp1 * m11 + tmp2 * m21 + tmp5 * m31);\n const t1 = (tmp1 * m01 + tmp6 * m21 + tmp9 * m31) -\n (tmp0 * m01 + tmp7 * m21 + tmp8 * m31);\n const t2 = (tmp2 * m01 + tmp7 * m11 + tmp10 * m31) -\n (tmp3 * m01 + tmp6 * m11 + tmp11 * m31);\n const t3 = (tmp5 * m01 + tmp8 * m11 + tmp11 * m21) -\n (tmp4 * m01 + tmp9 * m11 + tmp10 * m21);\n\n return m00 * t0 + m10 * t1 + m20 * t2 + m30 * t3;\n}\n\n/**\n * Computes the inverse of a 4-by-4 matrix. (same as inverse)\n * @param m - The matrix.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The inverse of m.\n */\nconst invert = inverse;\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nfunction multiply(a: Mat4Arg, b: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const a00 = a[0];\n const a01 = a[1];\n const a02 = a[2];\n const a03 = a[3];\n const a10 = a[ 4 + 0];\n const a11 = a[ 4 + 1];\n const a12 = a[ 4 + 2];\n const a13 = a[ 4 + 3];\n const a20 = a[ 8 + 0];\n const a21 = a[ 8 + 1];\n const a22 = a[ 8 + 2];\n const a23 = a[ 8 + 3];\n const a30 = a[12 + 0];\n const a31 = a[12 + 1];\n const a32 = a[12 + 2];\n const a33 = a[12 + 3];\n const b00 = b[0];\n const b01 = b[1];\n const b02 = b[2];\n const b03 = b[3];\n const b10 = b[ 4 + 0];\n const b11 = b[ 4 + 1];\n const b12 = b[ 4 + 2];\n const b13 = b[ 4 + 3];\n const b20 = b[ 8 + 0];\n const b21 = b[ 8 + 1];\n const b22 = b[ 8 + 2];\n const b23 = b[ 8 + 3];\n const b30 = b[12 + 0];\n const b31 = b[12 + 1];\n const b32 = b[12 + 2];\n const b33 = b[12 + 3];\n\n newDst[ 0] = a00 * b00 + a10 * b01 + a20 * b02 + a30 * b03;\n newDst[ 1] = a01 * b00 + a11 * b01 + a21 * b02 + a31 * b03;\n newDst[ 2] = a02 * b00 + a12 * b01 + a22 * b02 + a32 * b03;\n newDst[ 3] = a03 * b00 + a13 * b01 + a23 * b02 + a33 * b03;\n newDst[ 4] = a00 * b10 + a10 * b11 + a20 * b12 + a30 * b13;\n newDst[ 5] = a01 * b10 + a11 * b11 + a21 * b12 + a31 * b13;\n newDst[ 6] = a02 * b10 + a12 * b11 + a22 * b12 + a32 * b13;\n newDst[ 7] = a03 * b10 + a13 * b11 + a23 * b12 + a33 * b13;\n newDst[ 8] = a00 * b20 + a10 * b21 + a20 * b22 + a30 * b23;\n newDst[ 9] = a01 * b20 + a11 * b21 + a21 * b22 + a31 * b23;\n newDst[10] = a02 * b20 + a12 * b21 + a22 * b22 + a32 * b23;\n newDst[11] = a03 * b20 + a13 * b21 + a23 * b22 + a33 * b23;\n newDst[12] = a00 * b30 + a10 * b31 + a20 * b32 + a30 * b33;\n newDst[13] = a01 * b30 + a11 * b31 + a21 * b32 + a31 * b33;\n newDst[14] = a02 * b30 + a12 * b31 + a22 * b32 + a32 * b33;\n newDst[15] = a03 * b30 + a13 * b31 + a23 * b32 + a33 * b33;\n\n return newDst;\n}\n\n/**\n * Multiplies two 4-by-4 matrices with a on the left and b on the right (same as multiply)\n * @param a - The matrix on the left.\n * @param b - The matrix on the right.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix product of a and b.\n */\nconst mul = multiply;\n\n/**\n * Sets the translation component of a 4-by-4 matrix to the given\n * vector.\n * @param a - The matrix.\n * @param v - The vector.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The matrix with translation set.\n */\nfunction setTranslation(a: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? identity()) as T;\n if (a !== newDst) {\n newDst[ 0] = a[ 0];\n newDst[ 1] = a[ 1];\n newDst[ 2] = a[ 2];\n newDst[ 3] = a[ 3];\n newDst[ 4] = a[ 4];\n newDst[ 5] = a[ 5];\n newDst[ 6] = a[ 6];\n newDst[ 7] = a[ 7];\n newDst[ 8] = a[ 8];\n newDst[ 9] = a[ 9];\n newDst[10] = a[10];\n newDst[11] = a[11];\n }\n newDst[12] = v[0];\n newDst[13] = v[1];\n newDst[14] = v[2];\n newDst[15] = 1;\n return newDst;\n}\n\n///**\n// * Returns the translation component of a 4-by-4 matrix as a vector with 3\n// * entries.\n// * @param m - The matrix.\n// * @param dst - vector to hold result. If not passed a new one is created.\n// * @returns The translation component of m.\n// */\nfunction getTranslation(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n newDst[0] = m[12];\n newDst[1] = m[13];\n newDst[2] = m[14];\n return newDst;\n}\n\n/**\n * Returns an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @returns The axis component of m.\n */\nfunction getAxis(m: Mat4Arg, axis: number, dst?: T) {\n const newDst = (dst ?? vec3.create());\n const off = axis * 4;\n newDst[0] = m[off + 0];\n newDst[1] = m[off + 1];\n newDst[2] = m[off + 2];\n return newDst;\n}\n\n/**\n * Sets an axis of a 4x4 matrix as a vector with 3 entries\n * @param m - The matrix.\n * @param v - the axis vector\n * @param axis - The axis 0 = x, 1 = y, 2 = z;\n * @param dst - The matrix to set. If not passed a new one is created.\n * @returns The matrix with axis set.\n */\nfunction setAxis(m: Mat4Arg, v: Vec3Arg, axis: number, dst: T) {\n const newDst = (dst === m) ? dst : copy(m, dst);\n\n const off = axis * 4;\n newDst[off + 0] = v[0];\n newDst[off + 1] = v[1];\n newDst[off + 2] = v[2];\n return newDst;\n}\n\n///**\n// * Returns the scaling component of the matrix\n// * @param m - The Matrix\n// * @param dst - The vector to set. If not passed a new one is created.\n// */\nfunction getScaling(m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? vec3.create()) as T;\n\n const xx = m[0];\n const xy = m[1];\n const xz = m[2];\n const yx = m[4];\n const yy = m[5];\n const yz = m[6];\n const zx = m[8];\n const zy = m[9];\n const zz = m[10];\n\n newDst[0] = Math.sqrt(xx * xx + xy * xy + xz * xz);\n newDst[1] = Math.sqrt(yx * yx + yy * yy + yz * yz);\n newDst[2] = Math.sqrt(zx * zx + zy * zy + zz * zz);\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 0 to 1 in the z dimension.\n *\n * Note: If you pass `Infinity` for zFar then it will produce a projection matrix\n * returns -Infinity for Z when transforming coordinates with Z <= 0 and +Infinity for Z\n * otherwise.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */\nfunction perspective(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = Math.tan(Math.PI * 0.5 - 0.5 * fieldOfViewYInRadians);\n\n newDst[0] = f / aspect;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = f;\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (Number.isFinite(zFar)) {\n const rangeInv = 1 / (zNear - zFar);\n newDst[10] = zFar * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n } else {\n newDst[10] = -1;\n newDst[14] = -zNear;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the angular height\n * of the frustum, the aspect ratio, and the near and far clipping planes. The\n * arguments define a frustum extending in the negative z direction. The given\n * angle is the vertical angle of the frustum, and the horizontal angle is\n * determined to produce the given aspect ratio. The arguments near and far are\n * the distances to the near and far clipping planes. Note that near and far\n * are not z coordinates, but rather they are distances along the negative\n * z-axis. The matrix generated sends the viewing frustum to the unit box.\n * We assume a unit box extending from -1 to 1 in the x and y dimensions and\n * from 1 (at -zNear) to 0 (at -zFar) in the z dimension.\n *\n * @param fieldOfViewYInRadians - The camera angle from top to bottom (in radians).\n * @param aspect - The aspect ratio width / height.\n * @param zNear - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param zFar - The depth (negative z coordinate)\n * of the far clipping plane. (default = Infinity)\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The perspective matrix.\n */function perspectiveReverseZ(fieldOfViewYInRadians: number, aspect: number, zNear: number, zFar = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const f = 1 / Math.tan(fieldOfViewYInRadians * 0.5);\n\n newDst[ 0] = f / aspect;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n\n newDst[ 4] = 0;\n newDst[ 5] = f;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n\n newDst[ 8] = 0;\n newDst[ 9] = 0;\n newDst[11] = -1;\n\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (zFar === Infinity) {\n newDst[10] = 0;\n newDst[14] = zNear;\n } else {\n const rangeInv = 1 / (zFar - zNear);\n newDst[10] = zNear * rangeInv;\n newDst[14] = zFar * zNear * rangeInv;\n }\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 orthogonal transformation matrix that transforms from\n * the given the left, right, bottom, and top dimensions to -1 +1 in x, and y\n * and 0 to +1 in z.\n * @param left - Left side of the near clipping plane viewport.\n * @param right - Right side of the near clipping plane viewport.\n * @param bottom - Bottom of the near clipping plane viewport.\n * @param top - Top of the near clipping plane viewport.\n * @param near - The depth (negative z coordinate)\n * of the near clipping plane.\n * @param far - The depth (negative z coordinate)\n * of the far clipping plane.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The orthographic projection matrix.\n */\nfunction ortho(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[0] = 2 / (right - left);\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n newDst[4] = 0;\n newDst[5] = 2 / (top - bottom);\n newDst[6] = 0;\n newDst[7] = 0;\n\n newDst[8] = 0;\n newDst[9] = 0;\n newDst[10] = 1 / (near - far);\n newDst[11] = 0;\n\n newDst[12] = (right + left) / (left - right);\n newDst[13] = (top + bottom) / (bottom - top);\n newDst[14] = near / (near - far);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 0 to 1 in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustum(left: number, right: number, bottom: number, top: number, near: number, far: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n const dz = (near - far);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[10] = far / dz;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = near * far / dz;\n newDst[15] = 0;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 reverse-z perspective transformation matrix given the left, right,\n * top, bottom, near and far clipping planes. The arguments define a frustum\n * extending in the negative z direction. The arguments near and far are the\n * distances to the near and far clipping planes. Note that near and far are not\n * z coordinates, but rather they are distances along the negative z-axis. The\n * matrix generated sends the viewing frustum to the unit box. We assume a unit\n * box extending from -1 to 1 in the x and y dimensions and from 1 (-near) to 0 (-far) in the z\n * dimension.\n * @param left - The x coordinate of the left plane of the box.\n * @param right - The x coordinate of the right plane of the box.\n * @param bottom - The y coordinate of the bottom plane of the box.\n * @param top - The y coordinate of the right plane of the box.\n * @param near - The negative z coordinate of the near plane of the box.\n * @param far - The negative z coordinate of the far plane of the box.\n * @param dst - Output matrix. If not passed a new one is created.\n * @returns The perspective projection matrix.\n */\nfunction frustumReverseZ(left: number, right: number, bottom: number, top: number, near: number, far = Infinity, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const dx = (right - left);\n const dy = (top - bottom);\n\n newDst[ 0] = 2 * near / dx;\n newDst[ 1] = 0;\n newDst[ 2] = 0;\n newDst[ 3] = 0;\n newDst[ 4] = 0;\n newDst[ 5] = 2 * near / dy;\n newDst[ 6] = 0;\n newDst[ 7] = 0;\n newDst[ 8] = (left + right) / dx;\n newDst[ 9] = (top + bottom) / dy;\n newDst[11] = -1;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[15] = 0;\n\n if (far === Infinity) {\n newDst[10] = 0;\n newDst[14] = near;\n } else {\n const rangeInv = 1 / (far - near);\n newDst[10] = near * rangeInv;\n newDst[14] = far * near * rangeInv;\n }\n\n return newDst;\n}\n\nconst xAxis = vec3.create();\nconst yAxis = vec3.create();\nconst zAxis = vec3.create();\n\n/**\n * Computes a 4-by-4 aim transformation.\n *\n * This is a matrix which positions an object aiming down positive Z.\n * toward the target.\n *\n * Note: this is **NOT** the inverse of lookAt as lookAt looks at negative Z.\n *\n * @param position - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction aim(position: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(target, position, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = position[0]; newDst[13] = position[1]; newDst[14] = position[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 camera aim transformation.\n *\n * This is a matrix which positions an object aiming down negative Z.\n * toward the target.\n *\n * Note: this is the inverse of `lookAt`\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The aim matrix.\n */\nfunction cameraAim(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = xAxis[1]; newDst[ 2] = xAxis[2]; newDst[ 3] = 0;\n newDst[ 4] = yAxis[0]; newDst[ 5] = yAxis[1]; newDst[ 6] = yAxis[2]; newDst[ 7] = 0;\n newDst[ 8] = zAxis[0]; newDst[ 9] = zAxis[1]; newDst[10] = zAxis[2]; newDst[11] = 0;\n newDst[12] = eye[0]; newDst[13] = eye[1]; newDst[14] = eye[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Computes a 4-by-4 view transformation.\n *\n * This is a view matrix which transforms all other objects\n * to be in the space of the view defined by the parameters.\n *\n * @param eye - The position of the object.\n * @param target - The position meant to be aimed at.\n * @param up - A vector pointing up.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The look-at matrix.\n */\nfunction lookAt(eye: Vec3Arg, target: Vec3Arg, up: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n vec3.normalize(vec3.subtract(eye, target, zAxis), zAxis);\n vec3.normalize(vec3.cross(up, zAxis, xAxis), xAxis);\n vec3.normalize(vec3.cross(zAxis, xAxis, yAxis), yAxis);\n\n newDst[ 0] = xAxis[0]; newDst[ 1] = yAxis[0]; newDst[ 2] = zAxis[0]; newDst[ 3] = 0;\n newDst[ 4] = xAxis[1]; newDst[ 5] = yAxis[1]; newDst[ 6] = zAxis[1]; newDst[ 7] = 0;\n newDst[ 8] = xAxis[2]; newDst[ 9] = yAxis[2]; newDst[10] = zAxis[2]; newDst[11] = 0;\n\n newDst[12] = -(xAxis[0] * eye[0] + xAxis[1] * eye[1] + xAxis[2] * eye[2]);\n newDst[13] = -(yAxis[0] * eye[0] + yAxis[1] * eye[1] + yAxis[2] * eye[2]);\n newDst[14] = -(zAxis[0] * eye[0] + zAxis[1] * eye[1] + zAxis[2] * eye[2]);\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which translates by the given vector v.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translation matrix.\n */\nfunction translation(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = v[0]; newDst[13] = v[1]; newDst[14] = v[2]; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Translates the given 4-by-4 matrix by the given vector v.\n * @param m - The matrix.\n * @param v - The vector by\n * which to translate.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The translated matrix.\n */\nfunction translate(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const m30 = m[3 * 4 + 0];\n const m31 = m[3 * 4 + 1];\n const m32 = m[3 * 4 + 2];\n const m33 = m[3 * 4 + 3];\n\n if (m !== newDst) {\n newDst[ 0] = m00;\n newDst[ 1] = m01;\n newDst[ 2] = m02;\n newDst[ 3] = m03;\n newDst[ 4] = m10;\n newDst[ 5] = m11;\n newDst[ 6] = m12;\n newDst[ 7] = m13;\n newDst[ 8] = m20;\n newDst[ 9] = m21;\n newDst[10] = m22;\n newDst[11] = m23;\n }\n\n newDst[12] = m00 * v0 + m10 * v1 + m20 * v2 + m30;\n newDst[13] = m01 * v0 + m11 * v1 + m21 * v2 + m31;\n newDst[14] = m02 * v0 + m12 * v1 + m22 * v2 + m32;\n newDst[15] = m03 * v0 + m13 * v1 + m23 * v2 + m33;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the x-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationX(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = 1; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = c; newDst[ 6] = s; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = -s; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the x-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateX(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[4] = c * m10 + s * m20;\n newDst[5] = c * m11 + s * m21;\n newDst[6] = c * m12 + s * m22;\n newDst[7] = c * m13 + s * m23;\n newDst[8] = c * m20 - s * m10;\n newDst[9] = c * m21 - s * m11;\n newDst[10] = c * m22 - s * m12;\n newDst[11] = c * m23 - s * m13;\n\n if (m !== newDst) {\n newDst[ 0] = m[ 0];\n newDst[ 1] = m[ 1];\n newDst[ 2] = m[ 2];\n newDst[ 3] = m[ 3];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the y-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationY(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = 0; newDst[ 2] = -s; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = 1; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = s; newDst[ 9] = 0; newDst[10] = c; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the y-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateY(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m20 = m[2 * 4 + 0];\n const m21 = m[2 * 4 + 1];\n const m22 = m[2 * 4 + 2];\n const m23 = m[2 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 - s * m20;\n newDst[ 1] = c * m01 - s * m21;\n newDst[ 2] = c * m02 - s * m22;\n newDst[ 3] = c * m03 - s * m23;\n newDst[ 8] = c * m20 + s * m00;\n newDst[ 9] = c * m21 + s * m01;\n newDst[10] = c * m22 + s * m02;\n newDst[11] = c * m23 + s * m03;\n\n if (m !== newDst) {\n newDst[ 4] = m[ 4];\n newDst[ 5] = m[ 5];\n newDst[ 6] = m[ 6];\n newDst[ 7] = m[ 7];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the z-axis by the given angle.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotation matrix.\n */\nfunction rotationZ(angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c; newDst[ 1] = s; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = -s; newDst[ 5] = c; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = 1; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the z-axis by the given\n * angle.\n * @param m - The matrix.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction rotateZ(m: Mat4Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const m00 = m[0 * 4 + 0];\n const m01 = m[0 * 4 + 1];\n const m02 = m[0 * 4 + 2];\n const m03 = m[0 * 4 + 3];\n const m10 = m[1 * 4 + 0];\n const m11 = m[1 * 4 + 1];\n const m12 = m[1 * 4 + 2];\n const m13 = m[1 * 4 + 3];\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n\n newDst[ 0] = c * m00 + s * m10;\n newDst[ 1] = c * m01 + s * m11;\n newDst[ 2] = c * m02 + s * m12;\n newDst[ 3] = c * m03 + s * m13;\n newDst[ 4] = c * m10 - s * m00;\n newDst[ 5] = c * m11 - s * m01;\n newDst[ 6] = c * m12 - s * m02;\n newDst[ 7] = c * m13 - s * m03;\n\n if (m !== newDst) {\n newDst[ 8] = m[ 8];\n newDst[ 9] = m[ 9];\n newDst[10] = m[10];\n newDst[11] = m[11];\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nfunction axisRotation(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n newDst[ 0] = xx + (1 - xx) * c;\n newDst[ 1] = x * y * oneMinusCosine + z * s;\n newDst[ 2] = x * z * oneMinusCosine - y * s;\n newDst[ 3] = 0;\n newDst[ 4] = x * y * oneMinusCosine - z * s;\n newDst[ 5] = yy + (1 - yy) * c;\n newDst[ 6] = y * z * oneMinusCosine + x * s;\n newDst[ 7] = 0;\n newDst[ 8] = x * z * oneMinusCosine + y * s;\n newDst[ 9] = y * z * oneMinusCosine - x * s;\n newDst[10] = zz + (1 - zz) * c;\n newDst[11] = 0;\n newDst[12] = 0;\n newDst[13] = 0;\n newDst[14] = 0;\n newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which rotates around the given axis by the given\n * angle. (same as axisRotation)\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns A matrix which rotates angle radians\n * around the axis.\n */\nconst rotation = axisRotation;\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle.\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nfunction axisRotate(m: Mat4Arg, axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n let x = axis[0];\n let y = axis[1];\n let z = axis[2];\n const n = Math.sqrt(x * x + y * y + z * z);\n x /= n;\n y /= n;\n z /= n;\n const xx = x * x;\n const yy = y * y;\n const zz = z * z;\n const c = Math.cos(angleInRadians);\n const s = Math.sin(angleInRadians);\n const oneMinusCosine = 1 - c;\n\n const r00 = xx + (1 - xx) * c;\n const r01 = x * y * oneMinusCosine + z * s;\n const r02 = x * z * oneMinusCosine - y * s;\n const r10 = x * y * oneMinusCosine - z * s;\n const r11 = yy + (1 - yy) * c;\n const r12 = y * z * oneMinusCosine + x * s;\n const r20 = x * z * oneMinusCosine + y * s;\n const r21 = y * z * oneMinusCosine - x * s;\n const r22 = zz + (1 - zz) * c;\n\n const m00 = m[0];\n const m01 = m[1];\n const m02 = m[2];\n const m03 = m[3];\n const m10 = m[4];\n const m11 = m[5];\n const m12 = m[6];\n const m13 = m[7];\n const m20 = m[8];\n const m21 = m[9];\n const m22 = m[10];\n const m23 = m[11];\n\n newDst[ 0] = r00 * m00 + r01 * m10 + r02 * m20;\n newDst[ 1] = r00 * m01 + r01 * m11 + r02 * m21;\n newDst[ 2] = r00 * m02 + r01 * m12 + r02 * m22;\n newDst[ 3] = r00 * m03 + r01 * m13 + r02 * m23;\n newDst[ 4] = r10 * m00 + r11 * m10 + r12 * m20;\n newDst[ 5] = r10 * m01 + r11 * m11 + r12 * m21;\n newDst[ 6] = r10 * m02 + r11 * m12 + r12 * m22;\n newDst[ 7] = r10 * m03 + r11 * m13 + r12 * m23;\n newDst[ 8] = r20 * m00 + r21 * m10 + r22 * m20;\n newDst[ 9] = r20 * m01 + r21 * m11 + r22 * m21;\n newDst[10] = r20 * m02 + r21 * m12 + r22 * m22;\n newDst[11] = r20 * m03 + r21 * m13 + r22 * m23;\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Rotates the given 4-by-4 matrix around the given axis by the\n * given angle. (same as rotate)\n * @param m - The matrix.\n * @param axis - The axis\n * about which to rotate.\n * @param angleInRadians - The angle by which to rotate (in radians).\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The rotated matrix.\n */\nconst rotate = axisRotate;\n\n/**\n * Creates a 4-by-4 matrix which scales in each dimension by an amount given by\n * the corresponding entry in the given vector; assumes the vector has three\n * entries.\n * @param v - A vector of\n * three entries specifying the factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction scaling(v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = v[0]; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = v[1]; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = v[2]; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by an amount\n * given by the corresponding entry in the given vector; assumes the vector has\n * three entries.\n * @param m - The matrix to be modified.\n * @param v - A vector of three entries specifying the\n * factor by which to scale in each dimension.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction scale(m: Mat4Arg, v: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n\n newDst[ 0] = v0 * m[0 * 4 + 0];\n newDst[ 1] = v0 * m[0 * 4 + 1];\n newDst[ 2] = v0 * m[0 * 4 + 2];\n newDst[ 3] = v0 * m[0 * 4 + 3];\n newDst[ 4] = v1 * m[1 * 4 + 0];\n newDst[ 5] = v1 * m[1 * 4 + 1];\n newDst[ 6] = v1 * m[1 * 4 + 2];\n newDst[ 7] = v1 * m[1 * 4 + 3];\n newDst[ 8] = v2 * m[2 * 4 + 0];\n newDst[ 9] = v2 * m[2 * 4 + 1];\n newDst[10] = v2 * m[2 * 4 + 2];\n newDst[11] = v2 * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\n/**\n * Creates a 4-by-4 matrix which scales a uniform amount in each dimension.\n * @param s - the amount to scale\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaling matrix.\n */\nfunction uniformScaling(s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s; newDst[ 1] = 0; newDst[ 2] = 0; newDst[ 3] = 0;\n newDst[ 4] = 0; newDst[ 5] = s; newDst[ 6] = 0; newDst[ 7] = 0;\n newDst[ 8] = 0; newDst[ 9] = 0; newDst[10] = s; newDst[11] = 0;\n newDst[12] = 0; newDst[13] = 0; newDst[14] = 0; newDst[15] = 1;\n\n return newDst;\n}\n\n/**\n * Scales the given 4-by-4 matrix in each dimension by a uniform scale.\n * @param m - The matrix to be modified.\n * @param s - The amount to scale.\n * @param dst - matrix to hold result. If not passed a new one is created.\n * @returns The scaled matrix.\n */\nfunction uniformScale(m: Mat4Arg, s: number, dst?: T) {\n const newDst = (dst ?? new Ctor(16)) as T;\n\n newDst[ 0] = s * m[0 * 4 + 0];\n newDst[ 1] = s * m[0 * 4 + 1];\n newDst[ 2] = s * m[0 * 4 + 2];\n newDst[ 3] = s * m[0 * 4 + 3];\n newDst[ 4] = s * m[1 * 4 + 0];\n newDst[ 5] = s * m[1 * 4 + 1];\n newDst[ 6] = s * m[1 * 4 + 2];\n newDst[ 7] = s * m[1 * 4 + 3];\n newDst[ 8] = s * m[2 * 4 + 0];\n newDst[ 9] = s * m[2 * 4 + 1];\n newDst[10] = s * m[2 * 4 + 2];\n newDst[11] = s * m[2 * 4 + 3];\n\n if (m !== newDst) {\n newDst[12] = m[12];\n newDst[13] = m[13];\n newDst[14] = m[14];\n newDst[15] = m[15];\n }\n\n return newDst;\n}\n\nreturn {\n create,\n set,\n fromMat3,\n fromQuat,\n negate,\n copy,\n clone,\n equalsApproximately,\n equals,\n identity,\n transpose,\n inverse,\n determinant,\n invert,\n multiply,\n mul,\n setTranslation,\n getTranslation,\n getAxis,\n setAxis,\n getScaling,\n perspective,\n perspectiveReverseZ,\n ortho,\n frustum,\n frustumReverseZ,\n aim,\n cameraAim,\n lookAt,\n translation,\n translate,\n rotationX,\n rotateX,\n rotationY,\n rotateY,\n rotationZ,\n rotateZ,\n axisRotation,\n rotation,\n axisRotate,\n rotate,\n scaling,\n scale,\n uniformScaling,\n uniformScale,\n};\n\n}\n\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\nexport function getAPI(Ctor: Mat4Ctor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { QuatArg, QuatType } from './quat';\nimport { Mat3Arg } from './mat3.js';\nimport { Mat4Arg } from './mat4.js';\nimport { Vec3Arg } from './vec3.js';\nimport { getAPI as getVec3API } from './vec3-impl';\nimport { BaseArgType } from './types';\n\nexport { QuatArg, QuatType };\n\ntype QuatCtor = new (n: number) => T;\n\nexport type RotationOrder = 'xyz' | 'xzy' | 'yxz' | 'yzx' | 'zxy' | 'zyx';\n\n/**\n * Generates am typed API for Qud\n * */\nfunction getAPIImpl(Ctor: QuatCtor) {\n const vec3 = getVec3API(Ctor);\n\n/**\n * Creates a quat4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a Quat; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Quat\n * Also see {@link quat.create} and {@link quat.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Sets a quaternion from the given angle and axis,\n * then returns it.\n *\n * @param axis - the axis to rotate around\n * @param angleInRadians - the angle\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The quaternion that represents the given axis and angle\n **/\nfunction fromAxisAngle(axis: Vec3Arg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n const s = Math.sin(halfAngle);\n\n newDst[0] = s * axis[0];\n newDst[1] = s * axis[1];\n newDst[2] = s * axis[2];\n newDst[3] = Math.cos(halfAngle);\n\n return newDst;\n}\n\n/**\n * Gets the rotation axis and angle\n * @param q - quaternion to compute from\n * @param dst - Vec3 to hold result. If not passed in a new one is created.\n * @return angle and axis\n */\nfunction toAxisAngle(q: QuatArg, dst?: T): { angle: number, axis: T } {\n const newDst = (dst ?? vec3.create(3)) as T;\n\n const angle = Math.acos(q[3]) * 2;\n const s = Math.sin(angle * 0.5);\n if (s > utils.EPSILON) {\n newDst[0] = q[0] / s;\n newDst[1] = q[1] / s;\n newDst[2] = q[2] / s;\n } else {\n newDst[0] = 1;\n newDst[1] = 0;\n newDst[2] = 0;\n }\n\n return { angle, axis: newDst };\n}\n\n/**\n * Returns the angle in degrees between two rotations a and b.\n * @param a - quaternion a\n * @param b - quaternion b\n * @return angle in radians between the two quaternions\n */\nfunction angle(a: QuatArg, b: QuatArg) {\n const d = dot(a, b);\n return Math.acos(2 * d * d - 1);\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction multiply(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n const bx = b[0];\n const by = b[1];\n const bz = b[2];\n const bw = b[3];\n\n newDst[0] = ax * bw + aw * bx + ay * bz - az * by;\n newDst[1] = ay * bw + aw * by + az * bx - ax * bz;\n newDst[2] = az * bw + aw * bz + ax * by - ay * bx;\n newDst[3] = aw * bw - ax * bx - ay * by - az * bz;\n\n return newDst;\n}\n\n/**\n * Multiplies two quaternions\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nconst mul = multiply;\n\n/**\n * Rotates the given quaternion around the X axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateX(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bx = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qw * bx;\n newDst[1] = qy * bw + qz * bx;\n newDst[2] = qz * bw - qy * bx;\n newDst[3] = qw * bw - qx * bx;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Y axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateY(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const by = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw - qz * by;\n newDst[1] = qy * bw + qw * by;\n newDst[2] = qz * bw + qx * by;\n newDst[3] = qw * bw - qy * by;\n\n return newDst;\n}\n\n/**\n * Rotates the given quaternion around the Z axis by the given angle.\n * @param q - quaternion to rotate\n * @param angleInRadians - The angle by which to rotate\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction rotateZ(q: QuatArg, angleInRadians: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const halfAngle = angleInRadians * 0.5;\n\n const qx = q[0];\n const qy = q[1];\n const qz = q[2];\n const qw = q[3];\n\n const bz = Math.sin(halfAngle);\n const bw = Math.cos(halfAngle);\n\n newDst[0] = qx * bw + qy * bz;\n newDst[1] = qy * bw - qx * bz;\n newDst[2] = qz * bw + qw * bz;\n newDst[3] = qw * bw - qz * bz;\n\n return newDst;\n}\n\n/**\n * Spherically linear interpolate between two quaternions\n *\n * @param a - starting value\n * @param b - ending value\n * @param t - value where 0 = a and 1 = b\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the result of a * b\n */\nfunction slerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const ax = a[0];\n const ay = a[1];\n const az = a[2];\n const aw = a[3];\n\n let bx = b[0];\n let by = b[1];\n let bz = b[2];\n let bw = b[3];\n\n let cosOmega = ax * bx + ay * by + az * bz + aw * bw;\n\n if (cosOmega < 0) {\n cosOmega = -cosOmega;\n bx = -bx;\n by = -by;\n bz = -bz;\n bw = -bw;\n }\n\n let scale0;\n let scale1;\n\n if (1.0 - cosOmega > utils.EPSILON) {\n const omega = Math.acos(cosOmega);\n const sinOmega = Math.sin(omega);\n scale0 = Math.sin((1 - t) * omega) / sinOmega;\n scale1 = Math.sin(t * omega) / sinOmega;\n } else {\n scale0 = 1.0 - t;\n scale1 = t;\n }\n\n newDst[0] = scale0 * ax + scale1 * bx;\n newDst[1] = scale0 * ay + scale1 * by;\n newDst[2] = scale0 * az + scale1 * bz;\n newDst[3] = scale0 * aw + scale1 * bw;\n\n return newDst;\n}\n\n/**\n * Compute the inverse of a quaternion\n *\n * @param q - quaternion to compute the inverse of\n * @returns A quaternion that is the result of a * b\n */\nfunction inverse(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const a0 = q[0];\n const a1 = q[1];\n const a2 = q[2];\n const a3 = q[3];\n\n const dot = a0 * a0 + a1 * a1 + a2 * a2 + a3 * a3;\n const invDot = dot ? 1 / dot : 0;\n\n newDst[0] = -a0 * invDot;\n newDst[1] = -a1 * invDot;\n newDst[2] = -a2 * invDot;\n newDst[3] = a3 * invDot;\n\n return newDst;\n}\n\n/**\n * Compute the conjugate of a quaternion\n * For quaternions with a magnitude of 1 (a unit quaternion)\n * this returns the same as the inverse but is faster to calculate.\n *\n * @param q - quaternion to compute the conjugate of.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The conjugate of q\n */\nfunction conjugate(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -q[0];\n newDst[1] = -q[1];\n newDst[2] = -q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given rotation matrix.\n *\n * The created quaternion is not normalized.\n *\n * @param m - rotation matrix\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction fromMat(m: Mat3Arg | Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n /*\n 0 1 2\n 3 4 5\n 6 7 8\n\n 0 1 2\n 4 5 6\n 8 9 10\n */\n\n // Algorithm in Ken Shoemake's article in 1987 SIGGRAPH course notes\n // article \"Quaternion Calculus and Fast Animation\".\n const trace = m[0] + m[5] + m[10];\n\n if (trace > 0.0) {\n // |w| > 1/2, may as well choose w > 1/2\n const root = Math.sqrt(trace + 1); // 2w\n newDst[3] = 0.5 * root;\n const invRoot = 0.5 / root; // 1/(4w)\n\n newDst[0] = (m[6] - m[9]) * invRoot;\n newDst[1] = (m[8] - m[2]) * invRoot;\n newDst[2] = (m[1] - m[4]) * invRoot;\n } else {\n // |w| <= 1/2\n let i = 0;\n\n if (m[5] > m[0]) {\n i = 1;\n }\n if (m[10] > m[i * 4 + i]) {\n i = 2;\n }\n\n const j = (i + 1) % 3;\n const k = (i + 2) % 3;\n\n const root = Math.sqrt(m[i * 4 + i] - m[j * 4 + j] - m[k * 4 + k] + 1.0);\n newDst[i] = 0.5 * root;\n\n const invRoot = 0.5 / root;\n\n newDst[3] = (m[j * 4 + k] - m[k * 4 + j]) * invRoot;\n newDst[j] = (m[j * 4 + i] + m[i * 4 + j]) * invRoot;\n newDst[k] = (m[k * 4 + i] + m[i * 4 + k]) * invRoot;\n }\n\n return newDst;\n}\n\n/**\n * Creates a quaternion from the given euler angle x, y, z using the provided intrinsic order for the conversion.\n *\n * @param xAngleInRadians - angle to rotate around X axis in radians.\n * @param yAngleInRadians - angle to rotate around Y axis in radians.\n * @param zAngleInRadians - angle to rotate around Z axis in radians.\n * @param order - order to apply euler angles\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion representing the same rotation as the euler angles applied in the given order\n */\nfunction fromEuler(\n xAngleInRadians: number,\n yAngleInRadians: number,\n zAngleInRadians: number,\n order: RotationOrder,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const xHalfAngle = xAngleInRadians * 0.5;\n const yHalfAngle = yAngleInRadians * 0.5;\n const zHalfAngle = zAngleInRadians * 0.5;\n\n const sx = Math.sin(xHalfAngle);\n const cx = Math.cos(xHalfAngle);\n const sy = Math.sin(yHalfAngle);\n const cy = Math.cos(yHalfAngle);\n const sz = Math.sin(zHalfAngle);\n const cz = Math.cos(zHalfAngle);\n\n switch (order) {\n case 'xyz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'xzy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yxz':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz - sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n case 'yzx':\n newDst[0] = sx * cy * cz + cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zxy':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz + sx * sy * cz;\n newDst[3] = cx * cy * cz - sx * sy * sz;\n break;\n\n case 'zyx':\n newDst[0] = sx * cy * cz - cx * sy * sz;\n newDst[1] = cx * sy * cz + sx * cy * sz;\n newDst[2] = cx * cy * sz - sx * sy * cz;\n newDst[3] = cx * cy * cz + sx * sy * sz;\n break;\n\n default:\n throw new Error(`Unknown rotation order: ${order}`);\n }\n\n return newDst;\n}\n\n/**\n * Copies a quaternion. (same as {@link quat.clone})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is a copy of q\n */\nfunction copy(q: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = q[0];\n newDst[1] = q[1];\n newDst[2] = q[2];\n newDst[3] = q[3];\n\n return newDst;\n}\n\n/**\n * Clones a quaternion. (same as {@link quat.copy})\n * Also see {@link quat.create} and {@link quat.set}\n * @param q - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A copy of q.\n */\nconst clone = copy;\n\n/**\n * Adds two quaternions; assumes a and b have the same dimension.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the sum of a and b.\n */\nfunction add(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nfunction subtract(a: QuatArg, b: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two quaternions.\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns A quaternion that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Multiplies a quaternion by a scalar.\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction mulScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a quaternion by a scalar. (same as mulScalar)\n * @param v - The quaternion.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The scaled quaternion.\n */\nfunction divScalar(v: QuatArg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Computes the dot product of two quaternions\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns dot product\n */\nfunction dot(a: QuatArg, b: QuatArg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Performs linear interpolation on two quaternions.\n * Given quaternions a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @param t - Interpolation coefficient.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: QuatArg, b: QuatArg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Computes the length of quaternion\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nfunction length(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of quaternion (same as length)\n * @param v - quaternion.\n * @returns length of quaternion.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of quaternion\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nfunction lengthSq(v: QuatArg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of quaternion (same as lengthSq)\n * @param v - quaternion.\n * @returns square of the length of quaternion.\n */\nconst lenSq = lengthSq;\n\n/**\n * Divides a quaternion by its Euclidean length and returns the quotient.\n * @param v - The quaternion.\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns The normalized quaternion.\n */\nfunction normalize(v: QuatArg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n }\n\n return newDst;\n}\n\n/**\n * Check if 2 quaternions are approximately equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are approximately equal\n */\nfunction equalsApproximately(a: QuatArg, b: QuatArg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 quaternions are exactly equal\n * @param a - Operand quaternion.\n * @param b - Operand quaternion.\n * @returns true if quaternions are exactly equal\n */\nfunction equals(a: QuatArg, b: QuatArg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Creates an identity quaternion\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns an identity quaternion\n */\nfunction identity(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n}\n\nconst tempVec3 = vec3.create();\nconst xUnitVec3 = vec3.create();\nconst yUnitVec3 = vec3.create();\n\n/**\n * Computes a quaternion to represent the shortest rotation from one vector to another.\n *\n * @param aUnit - the start vector\n * @param bUnit - the end vector\n * @param dst - quaternion to hold result. If not passed in a new one is created.\n * @returns the result\n */\nfunction rotationTo(aUnit: Vec3Arg, bUnit: Vec3Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const dot = vec3.dot(aUnit, bUnit);\n if (dot < -0.999999) {\n vec3.cross(xUnitVec3, aUnit, tempVec3);\n if (vec3.len(tempVec3) < 0.000001) {\n vec3.cross(yUnitVec3, aUnit, tempVec3);\n }\n\n vec3.normalize(tempVec3, tempVec3);\n fromAxisAngle(tempVec3, Math.PI, newDst);\n\n return newDst;\n } else if (dot > 0.999999) {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 1;\n\n return newDst;\n } else {\n vec3.cross(aUnit, bUnit, tempVec3);\n\n newDst[0] = tempVec3[0];\n newDst[1] = tempVec3[1];\n newDst[2] = tempVec3[2];\n newDst[3] = 1 + dot;\n\n return normalize(newDst, newDst);\n }\n}\n\nconst tempQuat1 = new Ctor(4);\nconst tempQuat2 = new Ctor(4);\n\n/**\n * Performs a spherical linear interpolation with two control points\n *\n * @param a - the first quaternion\n * @param b - the second quaternion\n * @param c - the third quaternion\n * @param d - the fourth quaternion\n * @param t - Interpolation coefficient 0 to 1\n * @returns result\n */\nfunction sqlerp(\n a: QuatArg,\n b: QuatArg,\n c: QuatArg,\n d: QuatArg,\n t: number,\n dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n slerp(a, d, t, tempQuat1);\n slerp(b, c, t, tempQuat2);\n slerp(tempQuat1, tempQuat2, 2 * t * (1 - t), newDst);\n\n return newDst;\n}\n\nreturn {\n create,\n fromValues,\n set,\n fromAxisAngle,\n toAxisAngle,\n angle,\n multiply,\n mul,\n rotateX,\n rotateY,\n rotateZ,\n slerp,\n inverse,\n conjugate,\n fromMat,\n fromEuler,\n copy,\n clone,\n add,\n subtract,\n sub,\n mulScalar,\n scale,\n divScalar,\n dot,\n lerp,\n length,\n len,\n lengthSq,\n lenSq,\n normalize,\n equalsApproximately,\n equals,\n identity,\n rotationTo,\n sqlerp,\n};\n\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Quat4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Quat4`. In other words you can do this\n *\n * const v = quat4.cross(v1, v2); // Creates a new Quat4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = quat4.create();\n * quat4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. So for example\n *\n * quat4.cross(v1, v2, v1); // Puts the cross product of v1 x v2 in v1\n *\n */\nexport function getAPI(Ctor: QuatCtor) {\n let api = cache.get(Ctor);\n if (!api) {\n api = getAPIImpl(Ctor);\n cache.set(Ctor, api);\n }\n return api as API;\n}\n","/*\n * Copyright 2022 Gregg Tavares\n *\n * Permission is hereby granted, free of charge, to any person obtaining a\n * copy of this software and associated documentation files (the \"Software\"),\n * to deal in the Software without restriction, including without limitation\n * the rights to use, copy, modify, merge, publish, distribute, sublicense,\n * and/or sell copies of the Software, and to permit persons to whom the\n * Software is furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL\n * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING\n * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER\n * DEALINGS IN THE SOFTWARE.\n */\nimport * as utils from './utils.js';\nimport { Vec4Arg, Vec4Type } from './vec4';\nimport { Mat4Arg } from './mat4';\nimport { BaseArgType } from './types';\n\nexport { Vec4Arg, Vec4Type };\n\ntype Vec4Ctor = new (n: number) => T;\n\n/**\n * Generates am typed API for Vec4\n * */\nfunction getAPIImpl(Ctor: Vec4Ctor) {\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values.\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param w - Initial w value.\n * @returns the created vector\n */\nfunction create(x?: number, y?: number, z?: number, w?: number) {\n const newDst = new Ctor(4);\n if (x !== undefined) {\n newDst[0] = x;\n if (y !== undefined) {\n newDst[1] = y;\n if (z !== undefined) {\n newDst[2] = z;\n if (w !== undefined) {\n newDst[3] = w;\n }\n }\n }\n }\n return newDst;\n}\n\n/**\n * Creates a vec4; may be called with x, y, z to set initial values. (same as create)\n * @param x - Initial x value.\n * @param y - Initial y value.\n * @param z - Initial z value.\n * @param z - Initial w value.\n * @returns the created vector\n */\nconst fromValues = create;\n\n/**\n * Sets the values of a Vec4\n * Also see {@link vec4.create} and {@link vec4.copy}\n *\n * @param x first value\n * @param y second value\n * @param z third value\n * @param w fourth value\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector with its elements set.\n */\nfunction set(x: number, y: number, z: number, w: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = x;\n newDst[1] = y;\n newDst[2] = z;\n newDst[3] = w;\n\n return newDst;\n}\n\n/**\n * Applies Math.ceil to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the ceil of each element of v.\n */\nfunction ceil(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.ceil(v[0]);\n newDst[1] = Math.ceil(v[1]);\n newDst[2] = Math.ceil(v[2]);\n newDst[3] = Math.ceil(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.floor to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the floor of each element of v.\n */\nfunction floor(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.floor(v[0]);\n newDst[1] = Math.floor(v[1]);\n newDst[2] = Math.floor(v[2]);\n newDst[3] = Math.floor(v[3]);\n\n return newDst;\n}\n\n/**\n * Applies Math.round to each element of vector\n * @param v - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the round of each element of v.\n */\nfunction round(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.round(v[0]);\n newDst[1] = Math.round(v[1]);\n newDst[2] = Math.round(v[2]);\n newDst[3] = Math.round(v[3]);\n\n return newDst;\n}\n\n/**\n * Clamp each element of vector between min and max\n * @param v - Operand vector.\n * @param max - Min value, default 0\n * @param min - Max value, default 1\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that the clamped value of each element of v.\n */\nfunction clamp(v: Vec4Arg, min = 0, max = 1, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(max, Math.max(min, v[0]));\n newDst[1] = Math.min(max, Math.max(min, v[1]));\n newDst[2] = Math.min(max, Math.max(min, v[2]));\n newDst[3] = Math.min(max, Math.max(min, v[3]));\n\n return newDst;\n}\n\n/**\n * Adds two vectors; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a and b.\n */\nfunction add(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0];\n newDst[1] = a[1] + b[1];\n newDst[2] = a[2] + b[2];\n newDst[3] = a[3] + b[3];\n\n return newDst;\n}\n\n/**\n * Adds two vectors, scaling the 2nd; assumes a and b have the same dimension.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param scale - Amount to scale b\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the sum of a + b * scale.\n */\nfunction addScaled(a: Vec4Arg, b: Vec4Arg, scale: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + b[0] * scale;\n newDst[1] = a[1] + b[1] * scale;\n newDst[2] = a[2] + b[2] * scale;\n newDst[3] = a[3] + b[3] * scale;\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nfunction subtract(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] - b[0];\n newDst[1] = a[1] - b[1];\n newDst[2] = a[2] - b[2];\n newDst[3] = a[3] - b[3];\n\n return newDst;\n}\n\n/**\n * Subtracts two vectors.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A vector that is the difference of a and b.\n */\nconst sub = subtract;\n\n/**\n * Check if 2 vectors are approximately equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are approximately equal\n */\nfunction equalsApproximately(a: Vec4Arg, b: Vec4Arg): boolean {\n return Math.abs(a[0] - b[0]) < utils.EPSILON &&\n Math.abs(a[1] - b[1]) < utils.EPSILON &&\n Math.abs(a[2] - b[2]) < utils.EPSILON &&\n Math.abs(a[3] - b[3]) < utils.EPSILON;\n}\n\n/**\n * Check if 2 vectors are exactly equal\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns true if vectors are exactly equal\n */\nfunction equals(a: Vec4Arg, b: Vec4Arg): boolean {\n return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficient.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The linear interpolated result.\n */\nfunction lerp(a: Vec4Arg, b: Vec4Arg, t: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t * (b[0] - a[0]);\n newDst[1] = a[1] + t * (b[1] - a[1]);\n newDst[2] = a[2] + t * (b[2] - a[2]);\n newDst[3] = a[3] + t * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Performs linear interpolation on two vectors.\n * Given vectors a and b and interpolation coefficient vector t, returns\n * a + t * (b - a).\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param t - Interpolation coefficients vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns the linear interpolated result.\n */\nfunction lerpV(a: Vec4Arg, b: Vec4Arg, t: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] + t[0] * (b[0] - a[0]);\n newDst[1] = a[1] + t[1] * (b[1] - a[1]);\n newDst[2] = a[2] + t[2] * (b[2] - a[2]);\n newDst[3] = a[3] + t[3] * (b[3] - a[3]);\n\n return newDst;\n}\n\n/**\n * Return max values of two vectors.\n * Given vectors a and b returns\n * [max(a[0], b[0]), max(a[1], b[1]), max(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The max components vector.\n */\nfunction max(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.max(a[0], b[0]);\n newDst[1] = Math.max(a[1], b[1]);\n newDst[2] = Math.max(a[2], b[2]);\n newDst[3] = Math.max(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Return min values of two vectors.\n * Given vectors a and b returns\n * [min(a[0], b[0]), min(a[1], b[1]), min(a[2], b[2])].\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The min components vector.\n */\nfunction min(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = Math.min(a[0], b[0]);\n newDst[1] = Math.min(a[1], b[1]);\n newDst[2] = Math.min(a[2], b[2]);\n newDst[3] = Math.min(a[3], b[3]);\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction mulScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] * k;\n newDst[1] = v[1] * k;\n newDst[2] = v[2] * k;\n newDst[3] = v[3] * k;\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by a scalar. (same as mulScalar)\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nconst scale = mulScalar;\n\n/**\n * Divides a vector by a scalar.\n * @param v - The vector.\n * @param k - The scalar.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The scaled vector.\n */\nfunction divScalar(v: Vec4Arg, k: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0] / k;\n newDst[1] = v[1] / k;\n newDst[2] = v[2] / k;\n newDst[3] = v[3] / k;\n\n return newDst;\n}\n\n/**\n * Inverse a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nfunction inverse(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 1 / v[0];\n newDst[1] = 1 / v[1];\n newDst[2] = 1 / v[2];\n newDst[3] = 1 / v[3];\n\n return newDst;\n}\n\n/**\n * Invert a vector. (same as inverse)\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The inverted vector.\n */\nconst invert = inverse;\n\n/**\n * Computes the dot product of two vectors\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @returns dot product\n */\nfunction dot(a: Vec4Arg, b: Vec4Arg): number {\n return (a[0] * b[0]) + (a[1] * b[1]) + (a[2] * b[2]) + (a[3] * b[3]);\n}\n\n/**\n * Computes the length of vector\n * @param v - vector.\n * @returns length of vector.\n */\nfunction length(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n}\n\n/**\n * Computes the length of vector (same as length)\n * @param v - vector.\n * @returns length of vector.\n */\nconst len = length;\n\n/**\n * Computes the square of the length of vector\n * @param v - vector.\n * @returns square of the length of vector.\n */\nfunction lengthSq(v: Vec4Arg): number {\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n return v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3;\n}\n\n/**\n * Computes the square of the length of vector (same as lengthSq)\n * @param v - vector.\n * @returns square of the length of vector.\n */\nconst lenSq = lengthSq;\n\n/**\n * Computes the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nfunction distance(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return Math.sqrt(dx * dx + dy * dy + dz * dz + dw * dw);\n}\n\n/**\n * Computes the distance between 2 points (same as distance)\n * @param a - vector.\n * @param b - vector.\n * @returns distance between a and b\n */\nconst dist = distance;\n\n/**\n * Computes the square of the distance between 2 points\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nfunction distanceSq(a: Vec4Arg, b: Vec4Arg): number {\n const dx = a[0] - b[0];\n const dy = a[1] - b[1];\n const dz = a[2] - b[2];\n const dw = a[3] - b[3];\n return dx * dx + dy * dy + dz * dz + dw * dw;\n}\n\n/**\n * Computes the square of the distance between 2 points (same as distanceSq)\n * @param a - vector.\n * @param b - vector.\n * @returns square of the distance between a and b\n */\nconst distSq = distanceSq;\n\n/**\n * Divides a vector by its Euclidean length and returns the quotient.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The normalized vector.\n */\nfunction normalize(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const v0 = v[0];\n const v1 = v[1];\n const v2 = v[2];\n const v3 = v[3];\n const len = Math.sqrt(v0 * v0 + v1 * v1 + v2 * v2 + v3 * v3);\n\n if (len > 0.00001) {\n newDst[0] = v0 / len;\n newDst[1] = v1 / len;\n newDst[2] = v2 / len;\n newDst[3] = v3 / len;\n } else {\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n }\n\n return newDst;\n}\n\n/**\n * Negates a vector.\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns -v.\n */\nfunction negate(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = -v[0];\n newDst[1] = -v[1];\n newDst[2] = -v[2];\n newDst[3] = -v[3];\n\n return newDst;\n}\n\n/**\n * Copies a vector. (same as {@link vec4.clone})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nfunction copy(v: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = v[0];\n newDst[1] = v[1];\n newDst[2] = v[2];\n newDst[3] = v[3];\n\n return newDst;\n}\n\n/**\n * Clones a vector. (same as {@link vec4.copy})\n * Also see {@link vec4.create} and {@link vec4.set}\n * @param v - The vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns A copy of v.\n */\nconst clone = copy;\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nfunction multiply(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] * b[0];\n newDst[1] = a[1] * b[1];\n newDst[2] = a[2] * b[2];\n newDst[3] = a[3] * b[3];\n\n return newDst;\n}\n\n/**\n * Multiplies a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as mul)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of products of entries of a and b.\n */\nconst mul = multiply;\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length.\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nfunction divide(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = a[0] / b[0];\n newDst[1] = a[1] / b[1];\n newDst[2] = a[2] / b[2];\n newDst[3] = a[3] / b[3];\n\n return newDst;\n}\n\n/**\n * Divides a vector by another vector (component-wise); assumes a and\n * b have the same length. (same as divide)\n * @param a - Operand vector.\n * @param b - Operand vector.\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The vector of quotients of entries of a and b.\n */\nconst div = divide;\n\n/**\n * Zero's a vector\n * @param dst - vector to hold result. If not passed in a new one is created.\n * @returns The zeroed vector.\n */\nfunction zero(dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n newDst[0] = 0;\n newDst[1] = 0;\n newDst[2] = 0;\n newDst[3] = 0;\n\n return newDst;\n}\n\n\n/**\n * transform vec4 by 4x4 matrix\n * @param v - the vector\n * @param m - The matrix.\n * @param dst - optional vec4 to store result. If not passed a new one is created.\n * @returns the transformed vector\n */\nfunction transformMat4(v: Vec4Arg, m: Mat4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n const x = v[0];\n const y = v[1];\n const z = v[2];\n const w = v[3];\n\n newDst[0] = m[0] * x + m[4] * y + m[ 8] * z + m[12] * w;\n newDst[1] = m[1] * x + m[5] * y + m[ 9] * z + m[13] * w;\n newDst[2] = m[2] * x + m[6] * y + m[10] * z + m[14] * w;\n newDst[3] = m[3] * x + m[7] * y + m[11] * z + m[15] * w;\n\n return newDst;\n}\n\n\n/**\n * Treat a 4D vector as a direction and set it's length\n *\n * @param a The vec4 to lengthen\n * @param len The length of the resulting vector\n * @returns The lengthened vector\n */\nfunction setLength(a: Vec4Arg, len: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n normalize(a, newDst);\n return mulScalar(newDst, len, newDst);\n}\n\n/**\n * Ensure a vector is not longer than a max length\n *\n * @param a The vec4 to limit\n * @param maxLen The longest length of the resulting vector\n * @returns The vector, shortened to maxLen if it's too long\n */\nfunction truncate(a: Vec4Arg, maxLen: number, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n\n if (length(a) > maxLen) {\n return setLength(a, maxLen, newDst);\n }\n\n return copy(a, newDst);\n}\n\n/**\n * Return the vector exactly between 2 endpoint vectors\n *\n * @param a Endpoint 1\n * @param b Endpoint 2\n * @returns The vector exactly residing between endpoints 1 and 2\n */\nfunction midpoint(a: Vec4Arg, b: Vec4Arg, dst?: T) {\n const newDst = (dst ?? new Ctor(4)) as T;\n return lerp(a, b, 0.5, newDst);\n}\n\nreturn {\n create,\n fromValues,\n set,\n ceil,\n floor,\n round,\n clamp,\n add,\n addScaled,\n subtract,\n sub,\n equalsApproximately,\n equals,\n lerp,\n lerpV,\n max,\n min,\n mulScalar,\n scale,\n divScalar,\n inverse,\n invert,\n dot,\n length,\n len,\n lengthSq,\n lenSq,\n distance,\n dist,\n distanceSq,\n distSq,\n normalize,\n negate,\n copy,\n clone,\n multiply,\n mul,\n divide,\n div,\n zero,\n transformMat4,\n setLength,\n truncate,\n midpoint,\n};\n}\n\ntype API = ReturnType>;\n\nconst cache = new Map();\n\n/**\n *\n * Vec4 math functions.\n *\n * Almost all functions take an optional `newDst` argument. If it is not passed in the\n * functions will create a new `Vec4`. In other words you can do this\n *\n * const v = vec4.cross(v1, v2); // Creates a new Vec4 with the cross product of v1 x v2.\n *\n * or\n *\n * const v = vec4.create();\n * vec4.cross(v1, v2, v); // Puts the cross product of v1 x v2 in v\n *\n * The first style is often easier but depending on where it's used it generates garbage where\n * as there is almost never allocation with the second style.\n *\n * It is always safe to pass any vector as the destination. 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\ No newline at end of file diff --git a/docs/assets/highlight.css b/docs/assets/highlight.css index 6f2ae55..176f1f1 100644 --- a/docs/assets/highlight.css +++ b/docs/assets/highlight.css @@ -27,10 +27,10 @@ --dark-hl-12: #9CDCFE; --light-hl-13: #0000FF; --dark-hl-13: #CE9178; - --light-hl-14: #000000; - --dark-hl-14: #C8C8C8; - --light-hl-15: #267F99; - --dark-hl-15: #4EC9B0; + --light-hl-14: #267F99; + --dark-hl-14: #4EC9B0; + --light-hl-15: #000000; + --dark-hl-15: #C8C8C8; --light-code-background: #FFFFFF; --dark-code-background: #1E1E1E; } diff --git a/docs/index.html b/docs/index.html index 86e3933..522104d 100644 --- a/docs/index.html +++ b/docs/index.html @@ -2,7 +2,7 @@

Fast 3d math library for webgpu

Why another 3d math library?

+

Types

wgpu-matrix functions take any compatible type as input.

Examples:

+
const view = mat4.lookAt(        //  view is Float32Array
  [10, 20, 30],  // position
  [0, 5, 0],     // target
  [0, 1, 0],     // up
);

const view2 = mat4.lookAt(         //  view2 is Float32Array
  new Float32Array([10, 20, 30]),  // position
  new Float64Array([0, 5, 0],      // target
  [0, 1, 0],     // up
);
+
+ +

wgpu-matrix functions return the type passed as the destination or their default

const a = vec2.add([1, 2], [3, 4]);           // a is Float32Array
const b = vec2.add([1, 2], [3, 4], [0, 0]);   // b is number[]

const j = vec2d.add([1, 2], [3, 4]);          // j is Float64Array
const k = vec2d.add([1, 2], [3, 4], [0, 0]);  // b is number[]

const f32 = new Float32Array(2);
const x = vec2d.add([1, 2], [3, 4]);          // x is number[]
const y = vec2d.add([1, 2], [3, 4], f32);     // y is Float32Array
+
+ +

etc...

+

Note: You're unlikely to need any thing except mat3, mat4, quat, +vec2, vec3, and vec4 but, there are 3 sets of functions, +each one returning a different default

+
mat4.identity()   // returns Float32Array
mat4d.identity()  // returns Float64Array
mat4n.identity()  // returns number[]
+
+ +

Similarly there's mat3d, mat3n, quatd, quatn, +vec2d, vec2n, vec3d, vec3n, vec4d, vec4n.

+

Just to be clear, identity, like most functions, takes a destination so

+
const f32 = new Float32Array(16);
const f64 = new Float64Array(16);
const arr = new Array<number>(16).fill(0);

mat4.identity()      // returns Float32Array
mat4.identity(f32)   // returns Float32Array (f32)
mat4.identity(f64)   // returns Float64Array (f64)
mat4.identity(arr)   // returns number[] (arr)

mat4d.identity()     // returns Float64Array
mat4d.identity(f32)  // returns Float32Array (f32)
mat4d.identity(f64)  // returns Float64Array (f64)
mat4d.identity(arr)  // returns number[] (arr)

mat4n.identity()     // returns number[]
mat4n.identity(f32)  // returns Float32Array (f32)
mat4n.identity(f64)  // returns Float64Array (f64)
mat4n.identity(arr)  // returns number[] (arr)
+
+ +

The only difference between the sets of functions is what type they default to returning.

Notes

mat4.perspective, mat4.ortho, and mat4.frustum @@ -88,7 +109,7 @@

vec3 in this library uses 3 floats per but be aware that an array of vec3 in a Uniform Block or other structure in WGSL, each vec3 is padded to 4 floats! In other words, if you declare

-
struct Foo {
  bar: vec3<f32>[3];
};
+
struct Foo {
  bar: vec3<f32>[3];
};
 

 
 
then bar[0] is at byte offset 0, bar[1] at byte offset 16, bar[2] at byte offset 32.

@@ -120,20 +141,20 @@
 
Migration
2.x -> 3.x
In JavaScript there should be no difference in the API except for the removable of setDefaultType.

 
In TypeScript, 3.x should mostly be type compatible with 2.x.
 3.x is an attempt to fix the casting that was necessary in 2.x.

-
// 2.x
device.queue.writeData(buffer, 0, mat4.identity() as Float32Array);  // sadness! 😭

// 3.x
device.queue.writeData(buffer, 0, mat4.identity());  // Yay! 🎉
+
// 2.x
device.queue.writeData(buffer, 0, mat4.identity() as Float32Array);  // sadness! 😭

// 3.x
device.queue.writeData(buffer, 0, mat4.identity());  // Yay! 🎉
 

 
 
In TypeScript the differences are as follows

 
Functions have a default type but return what is passed to them as the dst.
In 3.x each function has a default type but if you pass it
 a destination it returns the type of the destination

-
mat4.identity()                       // returns Float32Array
mat4.identity(new Float32Array(16));  // returns Float32Array
mat4.identity(new Float64Array(16));  // returns Float32Array
mat4.identity(new Array(16));         // returns number[]
+
mat4.identity()                       // returns Float32Array
mat4.identity(new Float32Array(16));  // returns Float32Array
mat4.identity(new Float64Array(16));  // returns Float64Array
mat4.identity(new Array(16));         // returns number[]
 

 
-
Types are specific
const a: Mat4 = ...;    // a = Float32Array
const b: Mat4d = ...;   // b = Float64Array
const c: Mat4n = ...;   // c = number[]
+
Types are specific
const a: Mat4 = ...;    // a = Float32Array
const b: Mat4d = ...;   // b = Float64Array
const c: Mat4n = ...;   // c = number[]
 

 
 
This is means code like this

-
const position: Mat4 = [10, 20, 30];
+
const position: Mat4 = [10, 20, 30];
 

 
 
No longer works because Mat4 is a Float32Array.

@@ -147,7 +168,7 @@
 
  • Float64Array types: Mat3d, Mat4d, Quatd, Vec2d, Vec3d, Vec4d,
    • 
 
  • number[] types: Mat3n, Mat4n, Quatn, Vec2n, Vec3n, Vec4n
    • 
 
-
    There are 3 sets of functions, each one returning a different default
    mat4.identity()   // returns Float32Array
    mat4d.identity()  // returns Float64Array
    mat4n.identity()  // returns number[]
+
    There are 3 sets of functions, each one returning a different default
    mat4.identity()   // returns Float32Array
    mat4d.identity()  // returns Float64Array
    mat4n.identity()  // returns number[]
 
    
 
 
    Similarly there's mat3d, mat3n, quatd, quatn,
@@ -178,4 +199,4 @@
 http://localhost:8080/test/?src=true&grep=mat3.*?translate
 runs only tests with mat3 followed by translate in the name of test.
    
 
    License
    MIT
    
-
    Settings
    Member Visibility
    On This Page
    wgpu-matrix
    
\ No newline at end of file
+
    Settings
    Member Visibility
    On This Page
    wgpu-matrix
    
\ No newline at end of file
diff --git a/docs/modules/mat3.html b/docs/modules/mat3.html
index 3f120b7..4c9acd3 100644
--- a/docs/modules/mat3.html
+++ b/docs/modules/mat3.html
@@ -1,4 +1,5 @@
-mat3 | wgpu-matrix
    Namespace mat3
    Index
    Functions
    clone
+mat3 | wgpu-matrix
    Namespace mat3
    3x3 Matrix functions that default to returning Float32Array
    
+
    Index
    Functions
    clone
 copy
 create
 determinant
diff --git a/docs/modules/mat3d.html b/docs/modules/mat3d.html
index 483cfbb..29b9d70 100644
--- a/docs/modules/mat3d.html
+++ b/docs/modules/mat3d.html
@@ -1,4 +1,5 @@
-mat3d | wgpu-matrix
    Namespace mat3d
    Index
    Functions
    clone
+mat3d | wgpu-matrix
    Namespace mat3d
    3x3 Matrix functions that default to returning Float64Array
    
+
    Index
    Functions
    clone
 copy
 create
 determinant
diff --git a/docs/modules/mat3n.html b/docs/modules/mat3n.html
index 6515b59..dc40657 100644
--- a/docs/modules/mat3n.html
+++ b/docs/modules/mat3n.html
@@ -1,4 +1,5 @@
-mat3n | wgpu-matrix
    Namespace mat3n
    Index
    Functions
    clone
+mat3n | wgpu-matrix
    Namespace mat3n
    3x3 Matrix functions that default to returning number[]
    
+
    Index
    Functions
    clone
 copy
 create
 determinant
diff --git a/docs/modules/mat4.html b/docs/modules/mat4.html
index 1669023..11ff5ce 100644
--- a/docs/modules/mat4.html
+++ b/docs/modules/mat4.html
@@ -1,4 +1,5 @@
-mat4 | wgpu-matrix
    Namespace mat4
    Index
    Functions
    aim
+mat4 | wgpu-matrix
    Namespace mat4
    4x4 Matrix functions that default to returning Float32Array
    
+
    Index
    Functions
    aim
 axisRotate
 axisRotation
 cameraAim
diff --git a/docs/modules/mat4d.html b/docs/modules/mat4d.html
index 8f57d79..96536bc 100644
--- a/docs/modules/mat4d.html
+++ b/docs/modules/mat4d.html
@@ -1,4 +1,5 @@
-mat4d | wgpu-matrix
    Namespace mat4d
    Index
    Functions
    aim
+mat4d | wgpu-matrix
    Namespace mat4d
    4x4 Matrix functions that default to returning Float64Array
    
+
    Index
    Functions
    aim
 axisRotate
 axisRotation
 cameraAim
diff --git a/docs/modules/mat4n.html b/docs/modules/mat4n.html
index 5c6c1b7..0137e96 100644
--- a/docs/modules/mat4n.html
+++ b/docs/modules/mat4n.html
@@ -1,4 +1,5 @@
-mat4n | wgpu-matrix
    Namespace mat4n
    Index
    Functions
    aim
+mat4n | wgpu-matrix
    Namespace mat4n
    4x4 Matrix functions that default to returning number[]
    
+
    Index
    Functions
    aim
 axisRotate
 axisRotation
 cameraAim
diff --git a/docs/modules/quat.html b/docs/modules/quat.html
index fa1ec5b..ec6fccb 100644
--- a/docs/modules/quat.html
+++ b/docs/modules/quat.html
@@ -1,4 +1,5 @@
-quat | wgpu-matrix
    Namespace quat
    Index
    Functions
    add
+quat | wgpu-matrix
    Namespace quat
    Quaternion functions that default to returning Float32Array
    
+
    Index
    Functions
    add
 angle
 clone
 conjugate
diff --git a/docs/modules/quatd.html b/docs/modules/quatd.html
index cd6579f..d624704 100644
--- a/docs/modules/quatd.html
+++ b/docs/modules/quatd.html
@@ -1,4 +1,5 @@
-quatd | wgpu-matrix
    Namespace quatd
    Index
    Functions
    add
+quatd | wgpu-matrix
    Namespace quatd
    Quaternion functions that default to returning Float64Array
    
+
    Index
    Functions
    add
 angle
 clone
 conjugate
diff --git a/docs/modules/quatn.html b/docs/modules/quatn.html
index a702d86..863321c 100644
--- a/docs/modules/quatn.html
+++ b/docs/modules/quatn.html
@@ -1,4 +1,5 @@
-quatn | wgpu-matrix
    Namespace quatn
    Index
    Functions
    add
+quatn | wgpu-matrix
    Namespace quatn
    Quaternion functions that default to returning number[]
    
+
    Index
    Functions
    add
 angle
 clone
 conjugate
diff --git a/docs/modules/vec2.html b/docs/modules/vec2.html
index b04e76f..4104346 100644
--- a/docs/modules/vec2.html
+++ b/docs/modules/vec2.html
@@ -1,4 +1,5 @@
-vec2 | wgpu-matrix
    Namespace vec2
    Index
    Functions
    add
+vec2 | wgpu-matrix
    Namespace vec2
    Vec2 functions that default to returning Float32Array
    
+
    Index
    Functions
    add
 addScaled
 angle
 ceil
diff --git a/docs/modules/vec2d.html b/docs/modules/vec2d.html
index a772434..6a62b34 100644
--- a/docs/modules/vec2d.html
+++ b/docs/modules/vec2d.html
@@ -1,4 +1,5 @@
-vec2d | wgpu-matrix
    Namespace vec2d
    Index
    Functions
    add
+vec2d | wgpu-matrix
    Namespace vec2d
    Vec2 functions that default to returning Float64Array
    
+
    Index
    Functions
    add
 addScaled
 angle
 ceil
diff --git a/docs/modules/vec2n.html b/docs/modules/vec2n.html
index d62af0b..48da52b 100644
--- a/docs/modules/vec2n.html
+++ b/docs/modules/vec2n.html
@@ -1,4 +1,5 @@
-vec2n | wgpu-matrix
    Namespace vec2n
    Index
    Functions
    add
+vec2n | wgpu-matrix
    Namespace vec2n
    Vec2 functions that default to returning number[]
    
+
    Index
    Functions
    add
 addScaled
 angle
 ceil
diff --git a/docs/modules/vec3.html b/docs/modules/vec3.html
index c905272..f5cc721 100644
--- a/docs/modules/vec3.html
+++ b/docs/modules/vec3.html
@@ -1,4 +1,5 @@
-vec3 | wgpu-matrix
    Namespace vec3
    Index
    Functions
    add
+vec3 | wgpu-matrix
    Namespace vec3
    Vec3 functions that default to returning Float32Array
    
+
    Index
    Functions
    add
 addScaled
 angle
 ceil
diff --git a/docs/modules/vec3d.html b/docs/modules/vec3d.html
index f67fb67..37720b4 100644
--- a/docs/modules/vec3d.html
+++ b/docs/modules/vec3d.html
@@ -1,4 +1,5 @@
-vec3d | wgpu-matrix
    Namespace vec3d
    Index
    Functions
    add
+vec3d | wgpu-matrix
    Namespace vec3d
    Vec3 functions that default to returning Float64Array
    
+
    Index
    Functions
    add
 addScaled
 angle
 ceil
diff --git a/docs/modules/vec3n.html b/docs/modules/vec3n.html
index 3df38eb..d206618 100644
--- a/docs/modules/vec3n.html
+++ b/docs/modules/vec3n.html
@@ -1,4 +1,5 @@
-vec3n | wgpu-matrix
    Namespace vec3n
    Index
    Functions
    add
+vec3n | wgpu-matrix
    Namespace vec3n
    Vec3 functions that default to returning number[]
    
+
    Index
    Functions
    add
 addScaled
 angle
 ceil
diff --git a/docs/modules/vec4.html b/docs/modules/vec4.html
index 4ef5144..2c30df6 100644
--- a/docs/modules/vec4.html
+++ b/docs/modules/vec4.html
@@ -1,4 +1,5 @@
-vec4 | wgpu-matrix
    Namespace vec4
    Index
    Functions
    add
+vec4 | wgpu-matrix
    Namespace vec4
    Vec3 functions that default to returning Float32Array
    
+
    Index
    Functions
    add
 addScaled
 ceil
 clamp
diff --git a/docs/modules/vec4d.html b/docs/modules/vec4d.html
index f8686b6..0cd0a80 100644
--- a/docs/modules/vec4d.html
+++ b/docs/modules/vec4d.html
@@ -1,4 +1,5 @@
-vec4d | wgpu-matrix
    Namespace vec4d
    Index
    Functions
    add
+vec4d | wgpu-matrix
    Namespace vec4d
    Vec3 functions that default to returning Float64Array
    
+
    Index
    Functions
    add
 addScaled
 ceil
 clamp
diff --git a/docs/modules/vec4n.html b/docs/modules/vec4n.html
index c5c136c..f021fa9 100644
--- a/docs/modules/vec4n.html
+++ b/docs/modules/vec4n.html
@@ -1,4 +1,5 @@
-vec4n | wgpu-matrix
    Namespace vec4n
    Index
    Functions
    add
+vec4n | wgpu-matrix
    Namespace vec4n
    Vec3 functions that default to returning number[]
    
+
    Index
    Functions
    add
 addScaled
 ceil
 clamp
diff --git a/package-lock.json b/package-lock.json
index 41f7f10..713d0d2 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -1,12 +1,12 @@
 {
   "name": "wgpu-matrix",
-  "version": "3.0.1",
+  "version": "3.0.2",
   "lockfileVersion": 3,
   "requires": true,
   "packages": {
     "": {
       "name": "wgpu-matrix",
-      "version": "3.0.1",
+      "version": "3.0.2",
       "license": "MIT",
       "devDependencies": {
         "@rollup/plugin-terser": "^0.4.4",
diff --git a/package.json b/package.json
index 78b570c..ca7c50f 100644
--- a/package.json
+++ b/package.json
@@ -1,6 +1,6 @@
 {
   "name": "wgpu-matrix",
-  "version": "3.0.1",
+  "version": "3.0.2",
   "description": "fast matrix math library for WebGPU",
   "main": "dist/3.x/wgpu-matrix.module.js",
   "module": "dist/3.x/wgpu-matrix.module.js",
diff --git a/src/quat-impl.ts b/src/quat-impl.ts
index 09144ce..b8cc2e7 100644
--- a/src/quat-impl.ts
+++ b/src/quat-impl.ts
@@ -728,7 +728,7 @@ function normalize(v: QuatArg, dst?: T) {
     newDst[0] = 0;
     newDst[1] = 0;
     newDst[2] = 0;
-    newDst[3] = 0;
+    newDst[3] = 1;
   }
 
   return newDst;
diff --git a/src/wgpu-matrix.ts b/src/wgpu-matrix.ts
index 9bc0826..055a283 100644
--- a/src/wgpu-matrix.ts
+++ b/src/wgpu-matrix.ts
@@ -1,3 +1,7 @@
+/**
+ * Some docs
+ * @namespace wgpu-matrix
+ */
 import {BaseArgType, ZeroArray} from './types';
 import {Mat3Arg, Mat3Type, getAPI as getMat3API} from './mat3-impl';
 import {Mat4Arg, Mat4Type, getAPI as getMat4API} from './mat4-impl';
@@ -86,51 +90,105 @@ function wgpuMatrixAPI<
 }
 
 export const {
-  /** @namespace */
+  /**
+   * 4x4 Matrix functions that default to returning `Float32Array`
+   * @namespace
+   */
   mat4,
-  /** @namespace */
+  /**
+   * 3x3 Matrix functions that default to returning `Float32Array`
+   * @namespace
+   */
   mat3,
-  /** @namespace */
+  /**
+   * Quaternion functions that default to returning `Float32Array`
+   * @namespace
+   */
   quat,
-  /** @namespace */
+  /**
+   * Vec2 functions that default to returning `Float32Array`
+   * @namespace
+   */
   vec2,
-  /** @namespace */
+  /**
+   * Vec3 functions that default to returning `Float32Array`
+   * @namespace
+   */
   vec3,
-  /** @namespace */
+  /**
+   * Vec3 functions that default to returning `Float32Array`
+   * @namespace
+   */
   vec4,
 } = wgpuMatrixAPI<
   Mat3, Mat4, Quat, Vec2, Vec3, Vec4>(
     Float32Array, Float32Array, Float32Array, Float32Array, Float32Array, Float32Array);
 
 export const {
-  /** @namespace */
+  /**
+   * 4x4 Matrix functions that default to returning `Float64Array`
+   * @namespace
+   */
   mat4: mat4d,
-  /** @namespace */
+  /**
+   * 3x3 Matrix functions that default to returning `Float64Array`
+   * @namespace
+   */
   mat3: mat3d,
-  /** @namespace */
+  /**
+   * Quaternion functions that default to returning `Float64Array`
+   * @namespace
+   */
   quat: quatd,
-  /** @namespace */
+  /**
+   * Vec2 functions that default to returning `Float64Array`
+   * @namespace
+   */
   vec2: vec2d,
-  /** @namespace */
+  /**
+   * Vec3 functions that default to returning `Float64Array`
+   * @namespace
+   */
   vec3: vec3d,
-  /** @namespace */
+  /**
+   * Vec3 functions that default to returning `Float64Array`
+   * @namespace
+   */
   vec4: vec4d,
 } = wgpuMatrixAPI<
   Mat3d, Mat4d, Quatd, Vec2d, Vec3d, Vec4d>(
     Float64Array, Float64Array, Float64Array, Float64Array, Float64Array, Float64Array);
 
 export const {
-  /** @namespace */
+  /**
+   * 4x4 Matrix functions that default to returning `number[]`
+   * @namespace
+   */
   mat4: mat4n,
-  /** @namespace */
+  /**
+   * 3x3 Matrix functions that default to returning `number[]`
+   * @namespace
+   */
   mat3: mat3n,
-  /** @namespace */
+  /**
+   * Quaternion functions that default to returning `number[]`
+   * @namespace
+   */
   quat: quatn,
-  /** @namespace */
+  /**
+   * Vec2 functions that default to returning `number[]`
+   * @namespace
+   */
   vec2: vec2n,
-  /** @namespace */
+  /**
+   * Vec3 functions that default to returning `number[]`
+   * @namespace
+   */
   vec3: vec3n,
-  /** @namespace */
+  /**
+   * Vec3 functions that default to returning `number[]`
+   * @namespace
+   */
   vec4: vec4n,
 } = wgpuMatrixAPI<
   Mat3n, Mat4n, Quatn, Vec2n, Vec3n, Vec4n>(