Year: 2012
Type: preprint
Abstract: We show that in the Klein projective ball model of hyperbolic space, the hyperbolic Voronoi diagram is affine and amounts to clip a corresponding power diagram, requiring however algebraic arithmetic. By considering the lesser-known Beltrami hemisphere model of hyperbolic geometry, we overcome the arithmetic limitations of Klein construction. Finally, we characterize the bisectors and geodesics in the other Poincar\' e upper half-space, the Poincaré ball, and the Lorentz hyperboloid models, and discusses on degenerate cases for which the dual hyperbolic Delaunay complex is not a triangulation.
Source: arXiv (Cornell University)
Authors: Nielsen, Frank, Nock, Richard
Institution: Association for Computing Machinery
Language: English
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W203581761