Local Conditions for Triangulating Submanifolds of Euclidean Space
Discrete and Computational Geometry
We consider the following setting: suppose that we are given a manifold M in Rd with positive reach. Moreover assume that we have an embedded simplical complex A without boundary, whose vertex set lies on the manifold, is sufficiently dense and such that all simplices in A have sufficient quality. We prove that if, locally, interiors of the projection of the simplices onto the tangent space do not intersect, then A is a triangulation of the manifold, that is, they are homeomorphic.
Boissonnat, Jean Daniel; Dyer, Ramsay; Ghosh, Arijit; Lieutier, Andre; and Wintraecken, Mathijs, "Local Conditions for Triangulating Submanifolds of Euclidean Space" (2021). Journal Articles. 1835.
Open Access, Hybrid Gold, Green