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An Obstruction to Delaunay Triangulations in Riemannian Manifolds
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.
Cited literature [16 references]
https://hal.inria.fr/hal-01583073
Contributor : Jean-Daniel Boissonnat <>
Submitted on : Wednesday, September 6, 2017 - 4:38:17 PM
Last modification on : Friday, April 30, 2021 - 9:52:05 AM
Contributor : Jean-Daniel Boissonnat <>
Submitted on : Wednesday, September 6, 2017 - 4:38:17 PM
Last modification on : Friday, April 30, 2021 - 9:52:05 AM
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