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Further results on the hyperbolic Voronoi diagrams
In Euclidean geometry, it is well-known that the -order Voronoi diagram in
can be computed from the vertical projection of the -level of
an arrangement of hyperplanes tangent to a convex potential function in
: the paraboloid. Similarly, we report for the Klein ball
model of hyperbolic geometry such a {\em concave} potential function: the
northern hemisphere. Furthermore, we also show how to build the hyperbolic
-order diagrams as equivalent clipped power diagrams in . We
investigate the hyperbolic Voronoi diagram in the hyperboloid model and show
how it reduces to a Klein-type model using central projections.Comment: 6 pages, 2 figures (ISVD 2014