What is the Voronoi diagram of a square?

Consider a square, C:\qhull>rbox c D2 2 RBOX c D2 4 -0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 0.5 There's two ways to compute the Voronoi diagram: with facet merging or with joggle. With facet merging, the result is: C:\qhull>rbox c D2 | qvoronoi Qz Voronoi diagram by the convex hull of 5 points in 3-d: Number of Voronoi regions and at-infinity: 5 Number of Voronoi vertices: 1 Number of facets in hull: 5 Statistics for: RBOX c D2 | QVORONOI Qz Number of points processed: 5 Number of hyperplanes created: 7 Number of distance tests for qhull: 8 Number of merged facets: 1 Number of distance tests for merging: 29 CPU seconds to compute hull (after input): 0 C:\qhull>rbox c D2 | qvoronoi Qz o 2 2 5 1 -10.101 -10.101 0 0 2 0 1 2 0 1 2 0 1 2 0 1 0 C:\qhull>rbox c D2 | qvoronoi Qz Fv 4 4 0 1 0 1 4 0 2 0 1 4 1 3 0 1 4 2 3 0 1 There is one Voronoi vertex at the origin and rays from the origin along each of the coordinate axes. The last line '4 2 3 0 1' means that there is a ray that bisects input points ... more.

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