Local conditions for triangulating submanifolds of Euclidean space

Jean-Daniel Boissonnat (1, 2) , Ramsay Dyer (1, 2) , Arijit Ghosh (3) , André Lieutier (4) , Mathijs Wintraecken (1, 5)

1 DATASHAPE - Understanding the Shape of Data
2 COMUE UCA - COMUE Université Côte d'Azur (2015-2019)
3 ACMU - Advanced Computing and Microelectronics Unit [Kolkata]
4 Dassault Systèmes
5 IST Austria - Institute of Science and Technology [Klosterneuburg, Austria]

In this paper, we consider the following setting: suppose that we are given a manifold 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.

Mots clés: Computational Geometry; Computational Topology; Triangulation of Submanifolds

Domaines: Géométrie algorithmique [cs.CG]; Algorithme et structure de données [cs.DS]; Topologie algébrique [math.AT]; Topologie géométrique [math.GT]; Géométrie différentielle [math.DG]

Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh, André Lieutier, Mathijs Wintraecken. Local conditions for triangulating submanifolds of Euclidean space. 2019. ⟨hal-02267620⟩