How can I display a slice through a surface?

I have a surface which is an ellipsoid, and I would like to display the cross-section of the ellipsoid at specific planes.

Answer 1

[MathWorks Support Team]

The SLICE command requires a volume of data defined on a uniformly spaced grid. Since a surface is defined by a set of vertices (usually on a nonuniformly spaced grid), use the GRIDDATA3 function to fit the surface to a uniformly spaced grid. You can then use the SLICE function to plot a slice through this volume, as illustrated by the following example:

[x, y, z] = ellipsoid(0,0,0,10,10,10,20);
ti = -10:.25:10; 

[XI,YI, ZI] = meshgrid(ti,ti, ti);

v = ones(size(x));

V = griddata3(x,y,z,v,XI,YI, ZI);
figure;

h = surf(x, y, z); hold on

set(h, 'FaceAlpha', 0.2,'EdgeAlpha', 0.2)

h1 = slice(XI, YI, ZI, V, [], [9 0 -9], []);

for i = 1:numel(h1)

      hi = h1(i);

      cdata = get(hi, 'CData');

      cdata(~isnan(cdata))=1;

      set(hi, 'CData', cdata, 'EdgeColor', 'none')

end

The method described above works for a general surface, but the time required to fit the surface to a fine grid is large. Alternatively, if the surface has a mathematical definition, as in the case of the ellipsoid, you can calculate the volume directly, as in the following example:

xc = 0;

yc = 0;

zc = 0;

xr = 10;

yr = 10;

zr = 10;

[x,y,z] = ellipsoid(xc,yc,zc,xr,yr,zr,20);

ti = -10:.25:10; 

[XI,YI, ZI] = meshgrid(ti,ti, ti);

V = (XI - xc).^2/xr^2+(YI - yc).^2/yr^2+(ZI - zc).^2/zr^2;

V(V>1)=NaN;

figure;

h = surf(x, y, z); hold on

set(h, 'FaceAlpha', 0.2,'EdgeAlpha', 0.2)

h1 = slice(XI, YI, ZI, V, [], [9 0 -9], []);

for i = 1:numel(h1)

      hi = h1(i);

      cdata = get(hi, 'CData');

      cdata(~isnan(cdata))=1;

      set(hi, 'CData', cdata, 'EdgeColor', 'none')

end

This code displays three slices through an ellipsoid.

[Jonathan Kwang]

You can call figure() before plot to have each plot in 3 separate figures. Example:

figure()
plot(x,y)

figure()
plot(y,z)

figure()
plot(x,z)

Or you can have 3 separate plots in 1 figure. Example:

subplot(2,2,1);
plot(x,y);
title('x vs y');

subplot(2,2,2);
plot(y,z);
title('y vs z');

subplot(2,2,3);
plot(x,z);
title('x vs z');