Sampling random points from an implicitly defined surface in Python

Question

I have an implicitly defined hypersurface in R^3, given by the zero level set of some function F:

F(x,y,z) = 0.

This part may not matter but: I want to plot this surface using the answers given in this or this thread.

Now I want to take a random sample of points from this surface. Does anyone know the best way to do this?

Answer 1

Well, simple way would be:

1. Triangulate implicit surface. For implicit surface there are variations of marching cubes, I believe, already done.

2. Given list of triangles, compute total area A=Sum(A_i), and probabilities p_i = A_i/A. Probabilities would be normalized, Sum(p_i)=1

3. Sample particular triangle i using probabilities p_i. Numpy.random.choice should help.

4. Given selected triangle, generate uniform point in the triangle using Generate random locations within a triangular domain