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Local Criteria for Triangulation of Manifolds

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 verified in such a setting, they are expected to be of general use.
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Contributor : Jean-Daniel Boissonnat Connect in order to contact the contributor
Submitted on : Monday, May 28, 2018 - 3:38:07 PM
Last modification on : Saturday, November 5, 2022 - 3:51:21 AM
Long-term archiving on: : Wednesday, August 29, 2018 - 2:21:50 PM


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Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh, Mathijs Wintraecken. Local Criteria for Triangulation of Manifolds. International Symposium on Computational Geometry, Jun 2018, Budapest, Hungary. ⟨10.4230/LIPIcs.SoCG.2018.9⟩. ⟨hal-01801616⟩



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