Further results on the hyperbolic Voronoi diagrams [article]

Frank Nielsen, Richard Nock
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
more » ... e hyperbolic Voronoi diagram in the hyperboloid model and show how it reduces to a Klein-type model using central projections.
arXiv:1410.1036v1 fatcat:zcovdun6pnd6fbijdkffogpney