2013/04/30 by Jean-Daniel Boissonnat, JEAN-DANIEL BOISSONNAT, Ramsay Dyer +3 · 34 citations
Computer Science · Mathematics · #Bowyer–Watson algorithm #Chew's second algorithm #Computational Geometry and Mesh Generation #Constrained Delaunay triangulation #Delaunay triangulation #Geometric Analysis and Curvature Flows #Metric (unit) #Pitteway triangulation #Point set triangulation #Ruppert's algorithm #Topological and Geometric Data Analysis #cs.CG
paper · pdf · doi:10.1142/s0218195913600078
published in International Journal of Computational Geometry & Applications 23(04n05), 303-333 (World Scientific) · Displayed expressions in the statements of Thm 3.14 and Cor 4.18 are missing a factor of the dimension (m) in the denominator of the version published in IJCGA: it is corrected here
openalex publication_date 2013/08/01 · arxiv created 2015/05/06 · arxiv updated 2015/05/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We introduce a parametrized notion of genericity for Delaunay triangulations which, in particular, implies that the Delaunay simplices of δ-generic point sets are thick. Equipped with this notion, we study the stability of Delaunay triangulations under perturbations of the metric and of the vertex positions. We quantify the magnitude of the perturbations under which the Delaunay triangulation remains unchanged.