are you still working on this problem, I took an interest in it and made an attempt at finding a solution. 90% of the way there, I use my own delauny algorithm so it might not be as fast as others here are the results.
will post github later
Im currently working on the edge cases, (the black lines) in the diagram. The location for the center of the triangles can easily be calculated at this point, just need to add the code, then just a matter of choosing your preffered method to solve this problem. No voronoi as of yet but its a fairly easy step after all this.