Creating cells on sphere

HI Guys, 

I am having a real issue with a resent task. I have generated a series of explicit points on a sphere and I would like to use these points to create a voronoi like structure. Rather then the points being the centre of the cell I would like the points to be the location of like intersection. I have tried a couple of things but the results always end up being completely whack y. If anyone could help i would be really grateful. To be honest i am not sure if this should be in the Voronoi Section as I don't know if that method of triangulation is the most appropriate. 

Lots of Love Conor