Local criteria for triangulation of manifolds *

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

1 DATASHAPE - Understanding the Shape of Data
2 Algorithms and Complexity
3 Indian Statistical Institute [Kolkata]

We present criteria for establishing a triangulation of a manifold. Given a manifold M , a simplicial complex A, and a map H from the underlying space of A to M , our criteria are presented in local coordinate charts for M , and ensure that H is a homeomorphism. These criteria do not require a differentiable structure, or even an explicit metric on M. No Delaunay property of A is assumed. The result provides a triangulation guarantee for algorithms that construct a simplicial complex by working in local coordinate patches. Because the criteria are easily checked algorithmically, they are expected to be of general use.

Mots clés: manifold; simplicial complex; homeomorphism; triangulation

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

Jean-Daniel Boissonnat, Ramsay Dyer, Arijit Ghosh, Mathijs Wintraecken. Local criteria for triangulation of manifolds *. 2017. ⟨hal-01661230⟩