I don't think you can get even a polygon that is not convex, because by construction, you start out with a convex polygon (the whole space) and all areas you're clipping away from that are using lines/half-spaces perpendicular to the line connecting the two points. If you assume a metric space with a symmetric metric respecting the triangle inequality, I have the feeling that you encounter a contradiction fairly quickly, but I haven't written down any formal proof either :)

In reply to Re^4: Is it possible to get a 'hole' in a Veronoi diagram? by Corion
in thread Better maps with Math::Geometry::Voronoi, and a Challenge for Math Monks by samtregar

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