# Stability of Delaunay-type structures for manifolds: Extended abstract

1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of $\delta$-generic point sets are thick. Equipped with this notion, we study the stability of Delaunay triangulations under perturbations of the metric and of the vertex positions. We then show that, for any sufficiently regular submanifold of Euclidean space, and appropriate $\epsilon$ and $\delta$, any sample set which meets a localized $\delta$-generic $\epsilon$-dense sampling criteria yields a manifold intrinsic Delaunay complex which is equal to the restricted Delaunay complex.
Keywords :
Type de document :
Communication dans un congrès
Proceedings of the twenty-eighth annual symposium on Computational geometry, Jun 2012, The University of North Carolina at Chapel Hill, United States. pp.229-238, 2012, 〈10.1145/2261250.2261284〉

https://hal.inria.fr/hal-01108449
Contributeur : Jean-Daniel Boissonnat <>
Soumis le : jeudi 22 janvier 2015 - 17:12:00
Dernière modification le : samedi 27 janvier 2018 - 01:31:24

### Citation

Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh. Stability of Delaunay-type structures for manifolds: Extended abstract. Proceedings of the twenty-eighth annual symposium on Computational geometry, Jun 2012, The University of North Carolina at Chapel Hill, United States. pp.229-238, 2012, 〈10.1145/2261250.2261284〉. 〈hal-01108449〉

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