Voronoi Skeleton

Hey people!

I would really appreciate your help. I have a deadline in two weeks, and Im struggling with this issue.

OK, I took me a awhile but I could find a way to make a voronoi pattern 2d, which envelopes a brep. As you can see in image one. My question now is, how can i use the edges of those surface, and transform them into the second image? 

Tks a lot!