Is it possible to make a Voronoi diagram out of a non-simple convex hull set of points or a non-simple polygon?
I have a set of points that make up a convex hull, but within the set of points, there exists sets of points that form polygons that leave"holes" within the convex hull. I am not really sure how to better describe this problem I have encountered and I haven't seen anything definitive about NOT being able to make a Voronoi diagram or alternative solutions or simplifications to the problem to make the Voronoi diagram computable.
Subsume that you have a discrete point set. Then the Voronoi cell of any given point from that set is the region of those points of space, which are closer to that given point than to any other point of that set.
Using this definition you'd clearly see that any point of space is either closer to some point of that set, to some other, or exactly on the border between those regions. The set of those borders probably is what you call the Voronoi diagram. But that is clearly related to the set of regions of my above definition.
Especially there cannot be any region of space which does not belong to any of those Voronoi regions (except the borders), giving rise to such 'holes' you mention. And all this clearly is independent on whether the initial discrete point set has finite or infinite count.
--- rk