Generate random not overlapping triangles

In my example I never calculate the voronoi. I’m not making use of fortunes algorithm I’m just making use of line intersections, it does make use of a quad grid though to speed up the process. This will give you all center points and vertices of the triangles, though as I mentioned its not 100% accurate on the edges.

So just Delaunay. Which you can then use to calculate the voronoi.