Visualizing hyperbolic Voronoi diagrams

Frank Nielsen, Richard Nock

Abstract: We present an interactive software, HVD, that represents internally the k-order hyperbolic Voronoi diagram of a finite set of sites as an equivalent clipped power diagram. HVD allows users to interactively browse the hyperbolic Voronoi diagrams and renders simultaneously the diagram in the five standard models of hyperbolic geometry: Namely, the Poincaré disk, the Poincaré upper plane, the Klein disk, the Beltrami hemisphere and the Weierstrass hyperboloid.