# Carpetplot Class Example Plots

These are some examples plots made with the carpetplot class.

## Simple Example

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

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

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;
``` ## 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. A plot using exact data input and Meshgrids

```warning off; % Suppress warnings (optional)
a = linspace(1,100,30);
b = linspace(100,200,20);
[A B] = meshgrid(a,b);
X = A.^2+B;
Y = A+B;
o = carpetplot(A,B,X,Y);
``` Using the vectors for a and b has the same effect

```clf;
warning off; % Suppress warnings (optional)
a = linspace(1,100,30);
b = linspace(100,200,20);
[A,B] = meshgrid(a,b);
X = A.^2+B;
Y = A+B;
o = carpetplot(a,b,X,Y);
``` Scattered data

```clf;
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;
o = carpetplot(a,b,X,Y);
``` ## 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.

The following example 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;
clf;
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])
``` 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.

```clf;
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;
``` Use get and set to change the K Values. The Intersections will not allign vertically anymore.

```delete(arrowH,textH)

set(o,'K1',get(o,'K1')*3)

cheaterlegend(o,'northwest');
grid on
``` ## Multiple Plots

The carpetplot class supports multiple plots. They can just be plotted into one figure by using the hold on command.

```clf;
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);
snapnow; %Only needed for publishing
``` 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','--');
snapnow; %Only needed for publishing
``` 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.

```clear;
clf;

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 = lattice(o1,o2,o3,'lines');
set(lLines,'LineWidth',0.5);
``` ## Styles

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

```hold off;
clear;
clf;

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')
snapnow; %Only needed for publishing
``` ```o = carpetplot(A,B,X,'ko--');
label(o);
title('carpet plot with custom line spec')
snapnow; %Only needed for publishing
``` ```o = carpetplot(A,B,X);
label(o);
set(o.alines,'color',[1 0 0],'linestyle',':')
snapnow; %Only needed for publishing
``` ```o = carpetplot(A,B,X); label(o);
set(o,'style','standard');
title('Standard Style');
snapnow; %Only needed for publishing
set(o,'style','basic');
title('Basic Style');
snapnow; %Only needed for publishing
set(o,'style','minimal');
title('Minimal Style');
snapnow; %Only needed for publishing
```   ## 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

```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');
snapnow; %Only needed for publishing

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:');

snapnow; %Only needed for publishing
```  ## 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.

```clear;
clf;

% 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;
LandConstr = hatchedline(o,TW_Land,WS_Land,'r-');
TakeOffConstr = hatchedline(o,TW_takeoff,WS_takeoff,'g-');
secSegmentConstr = hatchedline(o,TW_secondSeg,WS_secondSeg,'y-');
CruiseConstr = hatchedline(o,TW_Cruise,WS_Cruise,'b-',-120);
o.showpoint(0.25,105);
``` ## Contourf Plot

This example uses the simple peaks() contour and the fill style for a constraint

```clear;
clf;
% 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
const = constraint(plotObject,'y<60 ','fill',[0.3 0.3 0.3]);
const = constraint(plotObject,'y>20','hatchedline','r-',45);

showpoint(plotObject,2,16);

% Move the label a little bit
snapnow; %Only needed for publishing
``` 