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Local Conditions for Triangulating Submanifolds of Euclidean Space

Abstract : We consider the following setting: suppose that we are given a manifold M in $${\mathbb {R}}^d$$ R d with positive reach. Moreover assume that we have an embedded simplical complex $${\mathcal {A}}$$ A without boundary, whose vertex set lies on the manifold, is sufficiently dense and such that all simplices in $${\mathcal {A}}$$ A have sufficient quality. We prove that if, locally, interiors of the projection of the simplices onto the tangent space do not intersect, then $${\mathcal {A}}$$ A is a triangulation of the manifold, that is, they are homeomorphic.
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Contributor : Jean-Daniel Boissonnat Connect in order to contact the contributor
Submitted on : Saturday, October 9, 2021 - 5:28:25 PM
Last modification on : Friday, February 4, 2022 - 3:16:32 AM
Long-term archiving on: : Monday, January 10, 2022 - 6:19:30 PM


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Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh, Andre Lieutier, Mathijs Wintraecken. Local Conditions for Triangulating Submanifolds of Euclidean Space. Discrete and Computational Geometry, Springer Verlag, 2021, 66 (2), pp.666-686. ⟨10.1007/s00454-020-00233-9⟩. ⟨hal-03372073⟩



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