Weak Witnesses for Delaunay triangulations of Submanifold

Dominique Attali (1) , Herbert Edelsbrunner (2) , Yuriy Mileyko (2)

1 GIPSA-GPIG - GIPSA - Géométrie, Perception, Images, Geste
2 Department of Computer Science

The main result of this paper is an extension of de Silva's Weak Delaunay Theorem to smoothly embedded curves and surfaces in Euclidean space. Assuming a sufficiently fine sampling, we prove that i + 1 points in the sample span an i-simplex in the restricted Delaunay triangulation iff every subset of i+1 points has a weak witness.

Mots clés: Computational geometry and topology; curves; surfaces; restricted Delaunay triangulations; witness complexes

Domaines: Géométrie algorithmique [cs.CG]

Dominique Attali, Herbert Edelsbrunner, Yuriy Mileyko. Weak Witnesses for Delaunay triangulations of Submanifold. ACM Symposium on Solid and Physical Modeling, Jun 2007, Beijing, China. pp.143-150. ⟨hal-00201055⟩