[amelius]

If the pointset is degenerate (e.g. 4 points on a circle), then you may get different local results in different copies of the space and the unioning may be difficult.

[Rhapso]

Ah, I'm an engineer not a theorist. Such degenerate input is unlikely to be a valid use case, can be detected, and I can reject it.

Wait until you see the actual heuristic I use for solving voronoi/delaunay in arbitrary topologies. I need to write a blog post on it anyways.

[amelius]

It's very easy to get 4 points on a circle. In 2d space just the four corners of a unit square would do it.

[Rhapso]

On a sphere or modulus space, that just becomes a K4, so it isn't even an edge case, it is the solution that the approximation would generate.

[amelius]

Yes, you definitely have to deal with it, in virtually any setup.