# 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.
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Conference papers
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https://hal.inria.fr/hal-01108449
Contributor : Jean-Daniel Boissonnat <>
Submitted on : Thursday, January 22, 2015 - 5:12:00 PM
Last modification on : Saturday, January 27, 2018 - 1:31:24 AM

### 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, ⟨10.1145/2261250.2261284⟩. ⟨hal-01108449⟩

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