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Journal Articles Discrete and Computational Geometry Year : 2021

## Local Conditions for Triangulating Submanifolds of Euclidean Space

Jean-Daniel Boissonnat
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Arijit Ghosh
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Andre Lieutier
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#### 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.

### Dates and versions

hal-03372073 , version 1 (09-10-2021)

### Identifiers

• HAL Id : hal-03372073 , version 1
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### Cite

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

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