Constructing Intrinsic Delaunay Triangulations of Submanifolds

Jean-Daniel Boissonnat 1 Ramsay Dyer 1, * Arijit Ghosh 2
* Corresponding author
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We describe an algorithm to construct an intrinsic Delaunay triangulation of a smooth closed submanifold of Euclidean space. Using results established in a companion paper on the stability of Delaunay triangulations on $\delta$-generic point sets, we establish sampling criteria which ensure that the intrinsic Delaunay complex coincides with the restricted Delaunay complex and also with the recently introduced tangential Delaunay complex. The algorithm generates a point set that meets the required criteria while the tangential complex is being constructed. In this way the computation of geodesic distances is avoided, the runtime is only linearly dependent on the ambient dimension, and the Delaunay complexes are guaranteed to be triangulations of the manifold.
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Submitted on : Tuesday, March 26, 2013 - 2:48:13 PM
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  • ARXIV : 1303.6493

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Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh. Constructing Intrinsic Delaunay Triangulations of Submanifolds. [Research Report] RR-8273, INRIA. 2013, pp.54. ⟨hal-00804878⟩

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