How do I plot the level sets of one function projected onto a surface, or how do I project contours onto a surface object in MATLAB?

I would like to plot the level sets of a function onto a surface. I have the equation defining the surface, as well as the set levels in term of the three variables, [X, Y, Z]

Answer 1

[MathWorks Support Team]

The ability to automatically have contour levels projected onto a surface is not available directly in MATLAB.

To work around this issue, read the commented example below:

The following example demonstrates the plotting of level sets of a function onto the surface as defined by another function, all in three variables.

[X,Y] = meshgrid([-2:.25:2]);

% Plotting the Z-values of the function whose level sets have

% to be determined

Z = X.*exp(-X.^2-Y.^2);

% Plotting the Z-values of the function on which the level

% sets have to be projected

Z1 = X.^2+Y.^2;

% Plot your contour

[cm,c]=contour(X,Y,Z,30);

% Plot the surface on which the level sets have to be projected

s=surface(X,Y,Z1,'EdgeColor',[.8 .8 .8],'FaceColor','none')

% Get the handle to the children i.e the contour lines of the contour

cv=get(c,'children');

% Extract the (X,Y) for each of the contours and recalculate the

% Z-coordinates on the surface on which to be projected.

for i=1:length(cv)

      cc = cv(i);

      xd=get(cc,'XData');

      yd=get(cc,'Ydata');

      zd=xd.^2+yd.^2;

      set(cc,'Zdata',zd);

end

grid off

view(-15,25)

colormap cool