diff --git a/Project.toml b/Project.toml
index 6831fd5..9f45ae7 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,7 +1,7 @@
 name = "LocalAnisotropies"
 uuid = "cb698b3a-2f1d-48b4-a1e9-ddc0b8f648e2"
 authors = ["Rafael Caixeta and contributors"]
-version = "0.6.2"
+version = "0.7.0"
 
 [deps]
 Distances = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
diff --git a/ext/LocalAnisotropiesMakieExt.jl b/ext/LocalAnisotropiesMakieExt.jl
index e2ba2fe..cd48b54 100644
--- a/ext/LocalAnisotropiesMakieExt.jl
+++ b/ext/LocalAnisotropiesMakieExt.jl
@@ -17,13 +17,15 @@ Makie.plottype(::LocalAnisotropy, ::LocalAnisotropies.SpatialData) =
 function pre_ellipsoid(lpars, geom, f)
     # pre process
     coords = LocalAnisotropies.coords_(geom)
+    mag = lpars.magnitude
+    mx = maximum
     D3 = size(coords, 1) >= 3
     x = coords[1, :]
     y = coords[2, :]
     z = D3 ? coords[3, :] : map(i -> 0, x)
     s =
-        D3 ? [f * Makie.Vec3f(i[1], i[2], i[3]) for i in eachcol(lpars.magnitude)] :
-        [f * Makie.Vec3f(i[1], i[2], i[2]) for i in eachcol(lpars.magnitude)]
+        D3 ? [f * Makie.Vec3f(i[1]/mx(i), i[2]/mx(i), i[3]/mx(i)) for i in eachcol(mag)] :
+        [f * Makie.Vec3f(i[1]/mx(i), i[2]/mx(i), i[2]/mx(i)) for i in eachcol(mag)]
     q = map(q -> Makie.Quaternion(q.q1, q.q2, q.q3, q.q0), lpars.rotation)
 
     x, y, z, s, q
diff --git a/src/estimators/kriging.jl b/src/estimators/kriging.jl
index 47dd5e3..a40f9ba 100644
--- a/src/estimators/kriging.jl
+++ b/src/estimators/kriging.jl
@@ -40,7 +40,12 @@ krig_estimator(model::KC_SKModel, localpar = nothing) = SimpleKriging(model.γ,
 neighs_localaniso(model::MWModels, m) = nothing
 neighs_localaniso(model::KCModels, m) = view(model.hdlocalaniso, m)
 
-function neighs_localaniso(localaniso::LocalAnisotropy, dom, neigh; method::Symbol=:KernelConvolution)
+function neighs_localaniso(
+    localaniso::LocalAnisotropy,
+    dom,
+    neigh;
+    method::Symbol = :KernelConvolution,
+)
     method != :KernelConvolution ? nothing : qmat(nnpars(localaniso, dom, neigh))
 end
 
diff --git a/src/estimators/sgs.jl b/src/estimators/sgs.jl
index 4472264..dfa619f 100644
--- a/src/estimators/sgs.jl
+++ b/src/estimators/sgs.jl
@@ -146,7 +146,7 @@ end
 
 function local_probmodel(probmodel, localaniso, hdlocalaniso)
     isnothing(hdlocalaniso) ? MW_SKModel(localaniso, probmodel.γ, probmodel.μ) :
-        KC_SKModel(localaniso, probmodel.γ, probmodel.μ, hdlocalaniso)
+    KC_SKModel(localaniso, probmodel.γ, probmodel.μ, hdlocalaniso)
 end
 
 function Meshes._pboxes(::Type{𝔼{N}}, points) where {N}
@@ -154,13 +154,13 @@ function Meshes._pboxes(::Type{𝔼{N}}, points) where {N}
     ℒ = lentype(p)
     cmin = fill(typemax(ℒ), N)
     cmax = fill(typemin(ℒ), N)
-  
+
     for p in points
-      c = getfield(coords(p), :coords)
-      for i in 1:N
-        cmin[i] = min(c[i], cmin[i])
-        cmax[i] = max(c[i], cmax[i])
-      end
+        c = getfield(coords(p), :coords)
+        for i = 1:N
+            cmin[i] = min(c[i], cmin[i])
+            cmax[i] = max(c[i], cmax[i])
+        end
     end
     Box(withcrs(p, Tuple(cmin)), withcrs(p, Tuple(cmax)))
-  end
\ No newline at end of file
+end
diff --git a/src/estimators/variograms.jl b/src/estimators/variograms.jl
index 29a1dfc..7d20a81 100644
--- a/src/estimators/variograms.jl
+++ b/src/estimators/variograms.jl
@@ -16,7 +16,8 @@ end
 
 qmat(L::LocalAnisotropy, i::Int) = qmat(localpair(L, i)...)
 qmat(L::LocalGeoData, i::Int) = qmat(localpair(L, i)...)
-qmat(L::Union{LocalAnisotropy,Nothing}) = isnothing(L) ? nothing : [qmat(L, i) for i = 1:nvals(L)]
+qmat(L::Union{LocalAnisotropy,Nothing}) =
+    isnothing(L) ? nothing : [qmat(L, i) for i = 1:nvals(L)]
 
 function mw_estimator(μ, γ, localpar)
     # get local Mahalanobis matrix
@@ -69,10 +70,3 @@ function kccov(γ::Variogram, xi, xj, Qi::AbstractMatrix, Qj::AbstractMatrix)
     Cij = (sill(γl) - γl(xi, xj))
     (det(Qi)^0.25) * (det(Qj)^0.25) * (det(Qij)^-0.5) * Cij
 end
-
-function localball(radii, rot, convention)
-    P, Λ = rotmat(radii, rot, convention)
-    Q = P' * Λ * P
-    Qs = ustrip.(Q ./ collect(radii)' .^ 2)
-    MetricBall(1.0, Mahalanobis(Symmetric(Qs)))
-end
diff --git a/src/parametrization/conventions.jl b/src/parametrization/conventions.jl
index f3e6b9f..3cd1fe9 100644
--- a/src/parametrization/conventions.jl
+++ b/src/parametrization/conventions.jl
@@ -98,6 +98,22 @@ function rotmat(
 
     # rotation matrix
     P = angle_to_dcm(angles..., rule.order)[SOneTo(N), SOneTo(N)]
-    !rule.extrinsic && (P = P')
+    rule.extrinsic && (P = P')
     P, Λ
 end
+
+function anisodistance(
+    semiaxes::AbstractVector,
+    angles::AbstractVector,
+    convention = :TaitBryanExtr;
+    rev = false,
+)
+    P, Λ = rotmat(semiaxes, angles, convention; rev)
+    Q = P' * Λ * P
+    Mahalanobis(Symmetric(Q))
+end
+
+function localball(radii, rot, convention)
+    metric_ = anisodistance(radii, rot, convention)
+    MetricBall(1.0, metric_)
+end
diff --git a/src/parametrization/conversions.jl b/src/parametrization/conversions.jl
index 2496597..2d66dab 100644
--- a/src/parametrization/conversions.jl
+++ b/src/parametrization/conversions.jl
@@ -51,18 +51,21 @@ function localanisotropies(
 
     if transf
         rule = convention isa Symbol ? rules[convention] : convention
-        rule.main == :y && (ranges = ranges[reverse(1:dim, 1, 2)])
+        if rule.main == :y
+            ranges = ranges[reverse(1:dim, 1, 2)]
+            rule = RotationRule(rule.order, rule.motion, rule.radian, :x, rule.extrinsic)
+        end
     end
 
     for i = 1:len
-        xranges =
-            [Tables.getcolumn(tab, x)[i] for x in ranges] ./ Tables.getcolumn(tab, ranges[1])[i]
+        vranges = [Tables.getcolumn(tab, x)[i] for x in ranges]
+        xranges = vranges ./ maximum(vranges)
         xrot = [Tables.getcolumn(tab, x)[i] for x in rotation]
 
         quat = if isquat
             Quaternion(xrot)
         else
-            P, Λ = rotmat(xranges, xrot, rule; rev = false)
+            P, Λ = rotmat(xranges, xrot, rule)
             size(P, 1) == 2 && (P = DCM([P[1, 1] P[1, 2] 0; P[2, 1] P[2, 2] 0; 0 0 1]))
             dcm_to_quat(P)
         end
@@ -196,7 +199,7 @@ function rotmat2angles(dcm::AbstractMatrix, convention::RotConvention)
     P = N == 2 ? DCM([P[1, 1] P[1, 2] 0; P[2, 1] P[2, 2] 0; 0 0 1]) : dcm
 
     rule = convention isa Symbol ? rules[convention] : convention
-    !rule.extrinsic && (P = P')
+    rule.extrinsic && (P = P')
     preangs = dcm_to_angle(DCM(P), rule.order)
     angles = [preangs.a1, preangs.a2, preangs.a3]
 
diff --git a/test/runtests.jl b/test/runtests.jl
index 426f960..a1e21a1 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,18 +1,66 @@
-using LocalAnisotropies
+using Distances
 using GeoStats
+using LocalAnisotropies
 using Test
-import LocalAnisotropies: rotmat
+import LocalAnisotropies: rotmat, anisodistance
 
 
 @testset "LocalAnisotropies.jl" begin
 
+    d₁ = anisodistance([1.0, 1.0], [0.0])
+    d₂ = anisodistance([1.0, 2.0], [0.0])
+    @test evaluate(d₁, [1.0, 0.0], [0.0, 0.0]) == evaluate(d₁, [0.0, 1.0], [0.0, 0.0])
+    @test evaluate(d₂, [1.0, 0.0], [0.0, 0.0]) != evaluate(d₂, [0.0, 1.0], [0.0, 0.0])
+
+    d₃ = anisodistance([1.0, 0.5, 0.5], [π / 4, 0.0, 0.0])
+    @test evaluate(d₃, [1.0, 1.0, 0.0], [0.0, 0.0, 0.0]) ≈ √2
+    @test evaluate(d₃, [-1.0, 1.0, 0.0], [0.0, 0.0, 0.0]) ≈ √8
+
+    # intrinsic conventions
+    gslib = anisodistance([50.0, 25.0, 5.0], [30.0, -30.0, 30.0], :GSLIB)
+    tait = anisodistance([25.0, 50.0, 5.0], [-π / 6, -π / 6, π / 6], :TaitBryanIntr)
+    euler = anisodistance(
+        [50.0, 25.0, 5.0],
+        [-deg2rad(78), -deg2rad(41), -deg2rad(50)],
+        :EulerIntr,
+    )
+    lpf = anisodistance([50.0, 25.0, 5.0], [78.0, 41.0, 50.0], :Leapfrog)
+    dm = anisodistance([50.0, 25.0, 5.0], [78.0, 41.0, 50.0], :Datamine)
+
+    @test evaluate(gslib, [1.0, 0.0, 0.0], [0.0, 0.0, 0.0]) ≈ 0.1325707358356285
+    @test evaluate(gslib, [0.0, 1.0, 0.0], [0.0, 0.0, 0.0]) ≈ 0.039051248379533283
+    @test evaluate(gslib, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0]) ≈ 0.15132745950421558
+
+    @test evaluate(gslib, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0]) ≈
+          evaluate(tait, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0])
+    @test evaluate(euler, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0]) ≈
+          evaluate(dm, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0])
+    @test evaluate(euler, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0]) ≈
+          evaluate(lpf, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0])
+    @test evaluate(euler, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0]) -
+          evaluate(gslib, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0]) < 10^-3
+
+    # extrinsic conventions
+    xtait = anisodistance([50.0, 25.0, 5.0], [π, 0, π / 2], :TaitBryanExtr)
+    xeuler = anisodistance([50.0, 25.0, 5.0], [-π / 2, -π / 2, -π / 2], :EulerExtr)
+
+    @test evaluate(xtait, [1.0, 0.0, 0.0], [0.0, 0.0, 0.0]) ≈ 0.20
+    @test evaluate(xtait, [0.0, 1.0, 0.0], [0.0, 0.0, 0.0]) ≈ 0.04
+    @test evaluate(xtait, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0]) ≈ 0.02
+
+    @test evaluate(xtait, [1.0, 0.0, 0.0], [0.0, 0.0, 0.0]) ≈
+          evaluate(xeuler, [1.0, 0.0, 0.0], [0.0, 0.0, 0.0])
+    @test evaluate(xtait, [0.0, 1.0, 0.0], [0.0, 0.0, 0.0]) ≈
+          evaluate(xeuler, [0.0, 1.0, 0.0], [0.0, 0.0, 0.0])
+    @test evaluate(xtait, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0]) ≈
+          evaluate(xeuler, [0.0, 0.0, 1.0], [0.0, 0.0, 0.0])
+
     # convert data to LocalAnisotropy
     dummy = georef(
         (az = 1:10, r1 = 1:10, r2 = 1:10),
         PointSet([(i / 2, (i + 1) / 2) for i = 1:2:19]),
     )
     pars = localanisotropies(dummy, [:az], [:r1, :r2], :GSLIB)
-    @test round(pars.rotation[1][4], digits = 4) ≈ 0.0087
 
     tabpars_quat = to_table(pars)
     tabpars_angs = to_table(pars, :GSLIB)
@@ -30,9 +78,11 @@ import LocalAnisotropies: rotmat
     # convert between different rotation conventions
     angs1 = convertangles([30, 30, 30], :GSLIB, :Datamine)
     angs2 = convertangles(angs1, :Datamine, :GSLIB)
-    rmat = rotmat([1, 1, 1], [30, 30, 30], :GSLIB)
-    @test all(rmat .≈ rotmat([1, 1, 1], angs1, :Datamine))
-    @test all(rmat .≈ rotmat([1, 1, 1], angs2, :GSLIB))
+    rmat, _ = rotmat([1, 1, 1], [30, 30, 30], :GSLIB)
+    dmat, _ = rotmat([1, 1, 1], angs1, :Datamine)
+    gmat, _ = rotmat([1, 1, 1], angs2, :GSLIB)
+    @test all(rmat .≈ dmat)
+    @test all(rmat .≈ gmat)
     angs_ = convertangles.(pars.rotation, :GSLIB)
     @test all([x[1] for x in angs_] .≈ 1:10)