Visualizing a toroidal surface in Matlab

Question

I have a problem which is twofold:

1. How do I plot a toroidal surface in MATLAB, given a major radius R and a minor radius a? To avoid confu

Answer 1

You can do this with surf - just create matrices with the x,y,z coordinates. The page you linked to has the trig equations to do this (they are exactly what you'd come up with on your own - I wrote the code below before checking your link).

R = 10;
a = 3;
tx=nan(41,21);
ty=nan(41,21);
tz=nan(41,21);
for j=1:21
  for i=1:41
    phi = (i-1)*2*pi/40;
    theta = (j-1)*2*pi/20;
    tx(i,j)= cos(phi) * (R+cos(theta)*a);
    ty(i,j)= sin(phi) * (R+cos(theta)*a);
    tz(i,j)= sin(theta)*a;
  end
end
figure
surf(tx,ty,tz)
axis equal

To distort the surface, replace the constant a with a matrix of the desired minor radius values, and index into that matrix - i.e. tz(i,j) = sin(theta)*distortion(i,j) (but in all dimensions, obviously).