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?

Is the surface bounded? Can you compute the bounds? Is the surface parametrisable? Do you care about the uniformity of the sampling distribution? Maybe choose random values for 2 out of 3 variables and then solve for the third. — Oscar Benjamin, Mar 21 '22 at 14:01

score 0 · Accepted Answer · answered Mar 21 '22 at 13:38

Well, simple way would be:

Triangulate implicit surface. For implicit surface there are variations of marching cubes, I believe, already done.
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
Sample particular triangle i using probabilities p_i. Numpy.random.choice should help.
Given selected triangle, generate uniform point in the triangle using Generate random locations within a triangular domain

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