2000 character limit reached
The hyperbolic Voronoi diagram in arbitrary dimension (1210.8234v4)
Published 31 Oct 2012 in cs.CG
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 Poincar\'e ball, and the Lorentz hyperboloid models, and discusses on degenerate cases for which the dual hyperbolic Delaunay complex is not a triangulation.
Collections
Sign up for free to add this paper to one or more collections.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
