Trimming Voronoi with Non rectangular shape.

I need the voronoi to trim down to the smaller non rectangular shape, while hopefully using the interior curve as the new edge for the shapes that are no longer closed after the trim, does that make sense?  Is this possible?  

To put it into further perspective, the interior shape is a UV surface of a 3d shape that im mapping the voronoi too.  I have it working with rectangle and square shapes, but haven't figured out how to keep the surface without stretching on these non rectangular shapes.

Thanks, let me know if you have any questions and thanks for the help.