The Stability of Delaunay Triangulations

Abstract

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.

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