Author:
Boissonnat Jean-Daniel,Dyer Ramsay,Ghosh Arijit,Lieutier Andre,Wintraecken Mathijs
Abstract
AbstractWe 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.
Funder
H2020 European Research Council
H2020 Marie Sklodowska-Curie Actions
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Theoretical Computer Science
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