The hyperbolic Voronoi diagram in arbitrary dimension

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.

18 pages, 3 figures

References in corpus (2)

• Hyperbolic Voronoi diagrams made easy
• On Approximating the Riemannian 1-Center

Cited by in corpus (3)

• On information projections between multivariate elliptical and location-scale families
• Approximation and bounding techniques for the Fisher-Rao distances between parametric statistical models
• Further results on the hyperbolic Voronoi diagrams