Voronoi closed curves on surface edge

Hi,

I'm doing a voronoi diagram on a non-planar surface, and I'm having trouble getting the resulting list of closed curves on the surface to include the ones at the edge. If I split the surface edge with the voronoi cells I can match the resulting list to the interior cells when the surface isn't complicated, but in the example below where some of the inner cell boundaries are single lines, the lists are too difficult to match up. I'm sure there's a better way to do this. Can someone please point me in the right direction?