Vertices2Volume

This function computes the volume of a 3D objects given its vertices X, Y, Z.

% Volume of a cylinder of radius 2, and height 3
r = 2; h = 3;
[X, Y, Z] = cylinder([0,r,r,0], 32);
Z([1,2],:) = 0; Z([3,4],:) = h;
figure(color = 'w')
% using matlab's convex hull function
[tri, vol1] = convhull(X, Y, Z);
subplot(1,2,1)
trisurf(tri, X, Y, Z, FaceColor='cyan')
title('Convex Hull')
axis equal
% new Vertices to volume function
vol2 = Vertices2Volume(X, Y, Z);
subplot(1,2,2)
surf(X, Y, Z, FaceColor='cyan'); 
title('Actual object')
axis equal;
% analytical solution
vol3 = pi*r^2*h;
error1 = 100*abs(vol1-vol3)/vol3;
error2 = 100*abs(vol2-vol3)/vol3;

% Volume of a sphere of radius 2,
r = 2;
[X, Y, Z] = sphere(32);
X = r*X; Y = r*Y; Z = r*Z;
figure(color = 'w')
% using matlab's convex hull function
[tri, vol1] = convhull(X, Y, Z);
subplot(1,2,1)
trisurf(tri, X, Y, Z, FaceColor='cyan')
title('Convex Hull')
axis equal
% new Vertices to volume function
vol2 = Vertices2Volume(X, Y, Z);
subplot(1,2,2)
surf(X, Y, Z, FaceColor='cyan'); 
title('Actual object')
axis equal;
% analytical solution
vol3 = 4*pi*r^3/3;
error1 = 100*abs(vol1-vol3)/vol3;
error2 = 100*abs(vol2-vol3)/vol3;


% Volume of a Torus with minor radius 1 and major radius 5
r = 1.5; R = 4; u = linspace(0, 2*pi, 33); 
z = r*sin(u); x = R + r*cos(u); 
v = linspace(0, 2*pi, 65)'; 
X = cos(v)*x; Y = sin(v)*x;
Z = ones(size(v))*z; 
figure(color = 'w')
% using matlab's convex hull function
[tri, vol1] = convhull(X, Y, Z);
subplot(1,2,1)
trisurf(tri, X, Y, Z, FaceColor='cyan')
title('Convex Hull')
axis equal
% new Vertices to volume function
vol2 = Vertices2Volume(X, Y, Z);
subplot(1,2,2)
surf(X, Y, Z, FaceColor='cyan'); 
title('Actual object')
axis equal;
% analytical solution
vol3 = 2*pi^2*r^2*R;
error1 = 100*abs(vol1-vol3)/vol3;
error2 = 100*abs(vol2-vol3)/vol3;