Parallel delaunay refinement with off-centers

Abstract

Off-centers were recently introduced as an alternative type of Steiner points to circum-centers for computing size-optimal quality guaranteed Delaunay triangulations. In this paper, we study the depth of the off-center insertion hierarchy. We prove that Delaunay refinement with off-centers takes only O(log(L/h)) parallel iterations, where L is the diameter of the domain, and h is the smallest edge in the initial triangulation. This is an improvement over the previously best known algorithm that runs in O(log2(L/h)) iterations. © Springer-Verlag 2004.