An Obstruction to Delaunay Triangulations in Riemannian Manifolds
Article Type
Research Article
Publication Title
Discrete and Computational Geometry
Abstract
Delaunay has shown that the Delaunay complex of a finite set of points P of Euclidean space Rm 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.
First Page
226
Last Page
237
DOI
10.1007/s00454-017-9908-5
Publication Date
1-1-2018
Recommended Citation
Boissonnat, Jean Daniel; Dyer, Ramsay; Ghosh, Arijit; and Martynchuk, Nikolay, "An Obstruction to Delaunay Triangulations in Riemannian Manifolds" (2018). Journal Articles. 1626.
https://digitalcommons.isical.ac.in/journal-articles/1626
Comments
All Open Access, Green