The hyperbolic Voronoi diagram in arbitrary dimension
Computational Geometry
2021-06-18 v4
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.
Cite
@article{arxiv.1210.8234,
title = {The hyperbolic Voronoi diagram in arbitrary dimension},
author = {Frank Nielsen and Richard Nock},
journal= {arXiv preprint arXiv:1210.8234},
year = {2021}
}
Comments
18 pages, 3 figures