Generate uniformly distributed points in a given Delaunay Triangulation DT?

I want to generate say 500 points inside a 3D Delaunay Triangulation and that they should be in best possible way be uniformly/evenly distributed inside the whole 3D space of Delaunay Triangulation.

If there is no good method to do this, then I could as well be okay with creating uniformly distributed points inside the 3D Convex Hull made out of the Delaunay Triangulation.

The motivation behind doing this is in the unanswered question here : http://www.mathworks.com/matlabcentral/answers/64331-common-volume-intersection-volume-between-two-delaunay-triangulations