An obstruction to Delaunay triangulations in Riemannian manifolds

Autor:	Boissonnat, Jean-Daniel, Dyer, Ramsay, Ghosh, Arijit, Martynchuk, Nikolay
Rok vydání:	2016
Předmět:	Computer Science - Computational Geometry Mathematics - Differential Geometry Mathematics - Geometric Topology 57R05 (Primary) 54B15 53B20 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Delaunay has shown that the Delaunay complex of a finite set of points $P$ of Euclidean space $\mathbb{R}^m$ triangulates the convex hull of $P$, provided that $P$ satisfies a mild genericity property. Voronoi diagrams and Delaunay complexes can be defined for arbitrary Riemannian manifolds. However, Delaunay's genericity assumption no longer guarantees that the Delaunay complex will yield a triangulation; stronger assumptions on $P$ are required. A natural one is to assume that $P$ is sufficiently dense. Although results in this direction have been claimed, we show that sample density alone is insufficient to ensure that the Delaunay complex triangulates a manifold of dimension greater than 2. Comment: This is a revision and extension of a note that appeared as an appendix in the (otherwise unpublished) report arXiv:1303.6493
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1612.02905 Zobrazit plný text záznamu View this record from Arxiv