# Local Conditions for Triangulating Submanifolds of Euclidean Space

1 DATASHAPE - Understanding the Shape of Data
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
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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Journal articles
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https://hal-amu.archives-ouvertes.fr/hal-03372073
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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### Citation

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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