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Further results on the hyperbolic Voronoi diagrams
[article]
2014
arXiv
pre-print
In Euclidean geometry, it is well-known that the k-order Voronoi diagram in R^d can be computed from the vertical projection of the k-level of an arrangement of hyperplanes tangent to a convex potential function in R^d+1: the paraboloid. Similarly, we report for the Klein ball model of hyperbolic geometry such a concave potential function: the northern hemisphere. Furthermore, we also show how to build the hyperbolic k-order diagrams as equivalent clipped power diagrams in R^d. We investigate
arXiv:1410.1036v1
fatcat:zcovdun6pnd6fbijdkffogpney