MATLAB: Is there a MATLAB function that can compute the area of the patch

isosurfaceMATLABsurfsurface

I use the ISOSURFACE function to generate a patch object:
[x,y,z,v] = flow;
p = patch(isosurface(x,y,z,v,-3));
isonormals(x,y,z,v,p)
set(p,'FaceColor','red','EdgeColor','none');
daspect([1 1 1])
view(3); 
camlight 
lighting gouraud
I would like to find the area of the patch "p".

Best Answer

There is no function which directly calculates the surface area of a patch object in MATLAB, however the calculations can be done in a fairly straightforward way using the 'Faces' and 'Vertices' properties of the patch object.
The surface area of the entire patch is then the sum of the areas of all the patch faces. The area of each triangular face can be computed with a cross product. Here is an example:
[x,y,z,v] = flow;
p = patch(isosurface(x,y,z,v,-3));
isonormals(x,y,z,v,p)
set(p,'FaceColor','red','EdgeColor','none');
daspect([1 1 1])
view(3); 
camlight 
lighting gouraud
verts = get(p, 'Vertices');
faces = get(p, 'Faces');
a = verts(faces(:, 2), :) - verts(faces(:, 1), :);
b = verts(faces(:, 3), :) - verts(faces(:, 1), :);
c = cross(a, b, 2);
area = 1/2 * sum(sqrt(sum(c.^2, 2)));
fprintf('\nThe surface area is %f\n\n', area);
If the patch object is constructed with faces that are not triangular (for example, they are rectangular), then each face can be broken down into triangular pieces (a rectangular face can be thought of as two triangular faces).
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