examples.m

function examples()
% EXAMPLES CarpetPlot Class Example Plots

set(gcf,'Renderer','OpenGL')

clf; example01; pause
clf; example02; pause
clf; example03; pause
clf; example04; pause
clf; example05; pause
clf; example06; pause
clf; example07; pause
clf; example08; pause
clf; example09; pause
clf; example10; pause
clf; example11; pause
clf; example12

end

function example01()
% In the beginning a simple example. More details about creating and
% labeling a carpet plot will be illustrated in the following examples.

a = 1:0.25:2;
b = 1:20:100;
[A, B] = meshgrid(a,b);
Y = A.*B;

o = CarpetPlot(A,B,Y);
label(o,'A-Axis','B-Axis')

grid on;

fprintf('Example 1 ...\n')
end

%%  Input Data
% The CarpetPlot class supports different kind of input data. The data can
% be exact (a matrix containing all datapoints) or scattered data. In this
% case the data points will be interpolated using TriScatteredInterp.
%
% There are two different types of carpet plots:
%
% *The cheater plot*
%  obj = CarpetPlot(a,b,Y)
%  obj = CarpetPlot(a,b,Y,z)
%
% *The (real) carpet plot*
%  obj = CarpetPlot(a,b,X,Y)
%  obj = CarpetPlot(a,b,X,Y,z)
%
% In case of exact data A and B can be eather vectors or meshgrids.
%
% If the input data are scattered data points a,b,(x) and y must be vectors
% with the corresponding coordinates of the datapoints.
%
% The z parameter is only used for the interpolation of whole carpet plots
% or lattice plots.
% 
%
% <<input.png>>
%
% 

function example02()
% A plot using exact data input and Meshgrids

a = linspace(1,100,30);
b = linspace(100,200,20);
[A, B] = meshgrid(a,b);
X = A.^2+B;
Y = A+B;

CarpetPlot(A,B,X,Y);

fprintf('Example 2 ...\n')
end

function example03()
% Using the vectors for a and b has the same effect

a = linspace(1,100,30);
b = linspace(100,200,20);
[A,B] = meshgrid(a,b);
X = A.^2+B;
Y = A+B;

CarpetPlot(a,b,X,Y);

fprintf('Example 3 ...\n')
end

function example04()
% Scattered data

a = [1 1 1 2 2 2 3 3 3];
b = [10 20 30 10 20 30 10 20 30];
X = a.^2+a;
Y = a+b;

CarpetPlot(a,b,X,Y);

fprintf('Example 4 ...\n')
end

%% Curve Fitting
% In the default case the interpolations of the carpet plot will be
% calculated and connected with a straight line.
%
% This *linear* curve will produce a cornered carpet if you do not have a lot of 
% intersections.
%
% To avoid this use the *spline* and *pchip* methods to produce curved 
% lines with the given intersections.
%
% Alternatively if you have a lot of data points but only wan't to vizualize
% a few intersections it is recommended to use  the exact methods 
% *epchip* or *espline* pr *elinear* as these methods consider all input
% datapoints for plotting.
%
function example05()
% Illustrates the different effects of the curve fitting methods.

a = linspace(-.5,1,50);
b = linspace(-1,6,14);
[A,B] = meshgrid(a,b);
Y = A.^3+B;
X = A-B*.2;
Y(1,4) = Y(1,4)-0.1;

hold on;

oinput = CarpetPlot(A,B,X,Y,'o','Color',[0.2 0.2 0.2]);
set(oinput,'aTick',linspace(-.5,1,50),'bTick',linspace(-1,6,14))
ospline = CarpetPlot(A,B,X,Y,'-','Color',[1 0 0]);
olinear = CarpetPlot(A,B,X,Y,'-','Color',[0.5 1 0.5]);
set(olinear,'curveFitting','linear','aTick',linspace(-.5,1,5))
set(ospline,'curveFitting','spline','aTick',linspace(-.5,1,5))
opchip = CarpetPlot(A,B,X,Y,'-','Color',[0 1 0]);
set(opchip,'curveFitting','pchip','aTick',linspace(-.5,1,5))
oepchip = CarpetPlot(A,B,X,Y,'-','Color',[0 0 1]);
set(oepchip,'curveFitting','epchip','aTick',linspace(-.5,1,5))
oespline = CarpetPlot(A,B,X,Y,'-','Color',[1 1 0]);
set(oespline,'curveFitting','espline','aTick',linspace(-.5,1,5))
oelinear = CarpetPlot(A,B,X,Y,'-','Color',[0 1 1]);
set(oelinear,'curveFitting','elinear','aTick',linspace(-.5,1,5))

legend([oinput olinear ospline opchip oepchip oespline oelinear] ...
    ,'Input Data','linear','Spline','Pchip','Exact pchip','Exact Spline','Exact Linear');

xlim([-0.32 0.1]); ylim([-1.17 -0.86])

fprintf('Example 5 ...\n');
end

%% As you can see all curve fitting methods have their trade offs. *pchip*
% and *spline* don't consider the points between the intersections. 
%
% *linear* just draws a straight line.
%
% The Exact Methods consider all points but are only usable if you have a
% lot of input data. *espline* especially with the data anomaly swings out
% a lot.
%
%% Cheater Plots
% Cheater plots do not have an x axis. The x-values for the vizualisation
% will calculated using 
%
%  X = k0 + a*K1 + b*K2
%
% The K values controll the plotting direction of the plot and as default
% the intersections align vertically. The allignement does only work if the
% a and b values are equally spaced.

function example06()

aValues = [1 1 1 2 2 2 3 3 3];
bValues = [10 15 20 10 15 20 10 15 20];
Y = aValues+bValues;
o = CarpetPlot(aValues,bValues,Y);
label(o);
set(o,'style','clean','alabelspacing',0.15);
[arrowH,textH] = cheaterlegend(o,'northwest');
grid on;

fprintf('Example 6, first part ...\n')

pause

% Use get and set to change the K Values. The Intersections will not allign
% vertically anymore.
delete(arrowH)
delete(textH)
set(o,'K1',get(o,'K1')*3)
cheaterlegend(o,'northwest');
grid on

fprintf('Example 6, second part ...\n')
end

%% Multiple Plots
function example07()
% The CarpetPlot class supports multiple plots. They can just be plotted
% into one figure by using the |hold on| command.

a =[1;2;3;1;2;3];
b =[10;10;10;30;30;30];
x = b-a.^3;
y = a.*b;

hold on;
o1 = CarpetPlot(a,b,x,y,10);
o2 = CarpetPlot(a,b,x+40,y+40,22);
o3 = CarpetPlot(a,b,x+190,y+15,34);

zlabel(o1,'Plot1 (z=10)');
zlabel(o2,'Plot2 (z=22)');
zlabel(o3,'Plot3 (z=34)');
[hlines, hmarkers, htext] = showpoint(o1,o2,o3,1.7,23);

fprintf('Example 7, first part ...\n')

pause

% A whole plot can be interpolated. The showpoint lines and text can be
% deleted using the handles.

delete(hlines); delete(hmarkers); delete(htext);
oi = interpolateplot(o1,o2,o3,30);
set(get(oi,'aLines'),'color',[0.5 0.5 0.5],'LineStyle','--');
set(get(oi,'blines'),'color',[0.5 0.5 0.5],'LineStyle','--');

fprintf('Example 7, second part ...\n')
end

function example08()
% Altough cheater plot's do not have an x-axis multiple carpets can be
% plotted using the lattice method. The x-axis shifting of the plot will
% represent the plot's z-value.

a = linspace(1,10,3);
b = linspace(10,30,3);
[A, B] = meshgrid(a,b);
X1 = A.*B;
X2 = (A.*B).*2;
X3 = (A.*B).*3;

hold on;
o1 = CarpetPlot(A,B,X1,-124);
set(o1,'style','standard');
o2 = CarpetPlot(A,B,X2,500);
set(o2,'k0',20,'style','standard')
o3 = CarpetPlot(A,B,X3,3000);
set(o3,'k0',40,'style','standard')

alabel(o3); blabel(o1);

lLines = o3.lattice(o1,o2,o3,'lines');
set(lLines,'LineWidth',0.5);

fprintf('Example 8 ...\n')
end

%% Styles
% The CarpetPlot class supports the possibility to customize the carpet
% plot with built in styles as well as with custom parameters.

function example09()
hold off;

a = linspace(1,10,3);
b = linspace(10,30,3);
[A, B] = meshgrid(a,b);
X = A+3.*B;

o = CarpetPlot(A,B,X);
label(o);
title('carpet plot with standard parameters')
fprintf('Example 9, standard parameters ...\n')
pause

o = CarpetPlot(A,B,X,'ko--');
label(o);
title('carpet plot with custom line spec')
fprintf('Example 9, custom line spec ...\n')
pause

o = CarpetPlot(A,B,X);
label(o);
set(o.alines,'color',[1 0 0],'linestyle',':')
fprintf('Example 9, custom line style ...\n')
pause

o = CarpetPlot(A,B,X); label(o); 
set(o,'style','standard');
title('Standard Style');
fprintf('Example 9, Standard Style ...\n')
pause

set(o,'style','basic');
title('Basic Style');
fprintf('Example 9, Basic Style ...\n')
pause

set(o,'style','minimal');
title('Minimal Style');
fprintf('Example 9, Minimal Style ...\n')

end

%% Transform coordinate Systems
% The carpetpot class has three build in functions to draw hatchedlines,
% line plots, and filled contours into the a b coordinate systems. If there
% are other plots needed it is possible to transform any vectors or
% matrixes into the carpet plot's coordinate system
function example10()

x = linspace(-0.5,10,200);
rng(0,'twister');
y = 10*cos(x)+ rand(1,200)+20;

hold off;
scatter(x,y)
title('Scatter Plot in the XY coordinate system');
fprintf('Example 10, scatter plot ...\n')
pause

a = linspace(-.5,10,5);
b = linspace(-1,40,4);
[A,B] = meshgrid(a,b);
Y = A.^2+B;
X = A-B*.2;

o = CarpetPlot(A,B,X,Y);
set(o,'curvefitting','pchip');
hold on;
[x, y] = o.abtoxy(x,y);
scatter(x,y)
title('Scatter Plot in the AB coordinate system');

hatchedline(o,linspace(-.5,10,5),ones(1,5)*32,'r-',-45);
hatchedline(o,linspace(-.5,10,5),ones(1,5)*10,'g-',45);
plot(o,linspace(-.5,10,5),ones(1,5)*20,'b:');

fprintf('Example 10, scatter on carpet plot ...\n')
end

%% Constraint Plot with fixed Weight trade study 
% This is a constraint plot common in aircraft design. The fixed weights of
% planes with different Wingloading [W/S] and Thrust/Weight-Ration [T/W] had been
% take in into account. The data was created using spreadsheet calculation.
function example11()

% Weight Estimations for different T/W and W/S
TW =  [0.1000    0.1200    0.1500    0.2000    0.2500    0.3000    0.1000    0.1200    0.1500    0.2000    0.2500 0.3000    0.1000    0.1200    0.1500    0.2000    0.2500    0.3000];
WS =  [60    60    60    60    60    60    90    90    90    90    90    90   120   120   120   120   120   120];
G0 =  10^4*[0.9901    1.0042    1.0252    1.0603    1.0953    1.1304    0.8957    0.9097    0.9308    0.9658    1.0009 1.0359    0.8485    0.8625    0.8835    0.9186    0.9537    0.9887];

% Constraint data
TW_Land = [ 0    0.0500    0.1000    0.1100    0.1200    0.1300    0.1400    0.1500    0.1600    0.1700    0.1800 0.1900    0.2000    0.3000];
WS_Land =[109.6875  109.6875  109.6875  109.6875  109.6875  109.6875  109.6875  109.6875  109.6875  109.6875  109.6875 109.6875  109.6875  109.6875];
TW_takeoff =[0    0.0250    0.0500    0.0750    0.1000    0.1250    0.1500    0.1750    0.2000    0.2250    0.2500 0.2750    0.3000    0.3250];
WS_takeoff =[0   10.7250   21.4500   32.1750   42.9000   53.6250   64.3500   75.0750   85.8000   96.5250  107.2500 117.9750  128.7000  139.4250];
TW_Cruise =[0.1000    0.1100    0.1200    0.1300    0.1400    0.1500    0.1600    0.1700    0.1800    0.1900    0.2000];
WS_Cruise =[109.0134   99.1031   90.8445   83.8565   77.8668   72.6756   68.1334   64.1256   60.5631   57.3755   54.5068];
TW_secondSeg =[0.1402    0.1402    0.1402    0.1402    0.1402    0.1402    0.1402    0.1402    0.1402];
WS_secondSeg =[60    70    80    90   100   120   130   140   150];

% Create the object and plot it
o = CarpetPlot(TW,WS,G0);

%Add some labels
alabel(o,'T/W');
blabel(o,'W/S [lb/ft²]');
ylabel('G0 [lb]');

set(o,'curveFitting','pchip','bLabelSpacing',0.2);

hold on;
hatchedline(o,TW_Land,WS_Land,'r-');
hatchedline(o,TW_takeoff,WS_takeoff,'g-');
hatchedline(o,TW_secondSeg,WS_secondSeg,'y-');
hatchedline(o,TW_Cruise,WS_Cruise,'b-',-120);

o.showpoint(0.25,105);

fprintf('Example 11 ...\n')
end

%% Contourf Plot
function example12()
% This example uses the simple |peaks()| contour and the fill style for a
% constraint

% Generate some Input Data
a =[1;2;3;1;2;3];
b =[10;10;10;30;30;30];
x = b-a.^3;
y = a.*b;

% Create the object and Plot
plotObject = CarpetPlot(a,b,x,y);
label(plotObject,'A-Axis','B-Axis')

% Change the curve Fitting and style
set(plotObject,'curvefitting','pchip','style','standard','blabelspacing',0.2,'barrowspacing',0.2);

% Add the contourf
hold on;
contourf(plotObject,1:0.1:3,10:1:30,peaks(21));

% Add some Constraints
try
    constraint(plotObject,'y<60 ','fill',[0.3 0.3 0.3]);
    constraint(plotObject,'y>20','hatchedline','r-',45);
catch ME
    switch ME.identifier
        case 'MATLAB:UndefinedFunction'
            warning('Undefined function in Example 12.\n')
            warning('This usually means no license for Matlab solve.');
        otherwise
            rethrow(ME)
    end
end

showpoint(plotObject,2,16);

fprintf('Example 12 ...\n')
end