My goal is to uniformly sample from a convex polytope. I know that for the simpler case, where I have to uniformly sample from a simplex, I can use Bayesian Bootstrap, discussed in these posts:
Uniform sampling from a simplex
Random vectors uniformely distributed into convex n-polytope
Therefore, I'm very interested in this approach. But I don't really know how to use Delaunay Triangulation here. What I have is a linear equation Ax = b and a non-negativity constraint that $x \geq \vec{0}$, and I want to sample x uniformly. Can someone tell me how to do the Delaunay Triangulation here? Thanks in advance!