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Local criteria for triangulation of manifolds *

Jean-Daniel Boissonnat 1 Ramsay Dyer 1 Arijit Ghosh 2, 3 Mathijs Wintraecken 1 
1 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
2 Algorithms and Complexity
MPII - Max-Planck-Institut für Informatik
Abstract : We present criteria for establishing a triangulation of a manifold. Given a manifold M , a simplicial complex A, and a map H from the underlying space of A to M , our criteria are presented in local coordinate charts for M , and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily checked algorithmically, they are expected to be of general use.
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Submitted on : Monday, December 11, 2017 - 6:38:00 PM
Last modification on : Saturday, November 5, 2022 - 3:51:21 AM


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Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh, Mathijs Wintraecken. Local criteria for triangulation of manifolds *. 2017. ⟨hal-01661230⟩



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