Contour plot for a non rectangular object

I have this case that I worked out in another software.

In the attached file, you can see the X,Y coordinates. The third column represents the results that I need to plot in a contour silimar to the one in the image above.

I tried several codes, but all of them plot on a rectagular area and/or not showing the same shape for the contour area. For example, the following code:

xyz = xlsread('data.xlsx');
x=xyz(2:end,1);
y=xyz(2:end,2);
z=xyz(2:end,3);
[X,Y]=meshgrid(min(x):max(x),min(y):max(y));
Z=griddata(x,y,z,X,Y);
contour(X,Y,Z)

Answer 1

[William Rose]

@Ghazwan,

[X,Y]=meshgrid(x,y) makes a grid where all the x values are the same across the grid, and likewise for yhe y values.

You can fix it by making your own X and Y instead of using meshgrid.

Nx=41; Ny=9;
dx=1; dy=1;  %adjust as desired
x=((0:Nx-1)-(Nx-1)/2)*dx; y=((0:Ny-1)-(Ny-1)/2)*dy;
[X,Y]=meshgrid(x,y);  %initial approximation
Z1=X+2*Y;
subplot(211); surf(X,Y,Z1); 
xlabel('X'); ylabel('Y'); axis equal; view(0,90)
%next: adjust the grid Y-values
Yadj=Y;
for i=1:Nx
    if i<=5||i>=37
        ymult=1;
    elseif i>=32
        ymult=(i-25)/12;
    elseif i<=10
        ymult=(17-i)/12;
    else
        ymult=0.5;
    end
    Yadj(:,i)=ymult*Y(:,i);
end
subplot(212); surf(X,Yadj,Z1); 
xlabel('X'); ylabel('Yadj'); axis equal; view(0,90)

It works. The code to adjust the y-values is not very elegant, but it demonstrates the possibilities for creating a non-retangular grid.

[William Rose]

@Ghazwan, you can use this approach to make a surface plot with polar coordinates:

Nh=36; Nr=9;            %grid dimensions: angle, radius
R=2;                    %max radius, adjust as desired
dr=R/(Nr-1);            %delta r
theta=(0:Nh)*2*pi/Nh;   %vector of angles
r=0:dr:R;               %vector of radii
[Radius,Theta]=meshgrid(r,theta);   %grid arrays
Z=cos(Theta).*sin(pi*Radius/R)/2;   %compute Z=Z(r,theta)
X=Radius.*cos(Theta);   %X cooridnates for plotting
Y=Radius.*sin(Theta);   %Y coordinates for plotting
surf(X,Y,Z);            %plot the surface
xlabel('X'); ylabel('Y'); zlabel('Z'); axis equal;

It is a start for polar grid plot.

[William Rose]

@Ghazwan,

You can also make a grid on an annulus, by a slight modificaiton of the code above:

Nh=72; Nr=9;            %grid dimensions: angle, radius
Rin=1; Rout=2;          %max radius, adjust as desired
dr=(Rout-Rin)/(Nr-1);   %delta r
theta=(0:Nh)*2*pi/Nh;   %vector of angles
r=Rin:dr:Rout;          %vector of radii
[Radius,Theta]=meshgrid(r,theta);   %grid arrays
Z=cos(2*Theta).*sin(pi*(Radius-Rin)/(Rout-Rin));   %compute Z=Z(r,theta)
X=Radius.*cos(Theta);   %X cooridnates for plotting
Y=Radius.*sin(Theta);   %Y coordinates for plotting
surf(X,Y,Z,'EdgeColor','none');  %plot surface
xlabel('X'); ylabel('Y'); zlabel('Z'); axis equal; view(0,90)

Try it.

[Ghazwan]

Thank you, William. This is excellent.

Your code gave me a good idea of what to do next. After I generate the proper coordinate array, I will interpolate the original contour data into the new array. This way, I can ensure that the contour data will get appropriately mapped into the new coordinate points.

[William Rose]

@Ghazwan, you are welcome. Your plan sounds good.