![]() ![]() ![]() We can do this in two different ways, which both lead to the degenerate case in your diagram. To visualise what I'm talking about, consider starting with four less regularly spaced points (such that we start off with only degree-3 vertices) and gradually translating them into their regular positions. ![]() The issue is that it's arbitrary which of the two possible edges you pick, because the zero-length edge has no associated direction. But that edge should still have a corresponding edge in the Delaunay triangulation. That means there is a zero-length edge between them. A vertex with degree 4 (or more) can only happen when two (or more) vertices coincide. If you generate a Voronoi diagram for an irregular point cloud, every vertex will have degree 3. The centre point in your diagram is a degenerate edge of the Voronoi diagram. ![]()
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