Lepp terminal centroid method for quality triangulation

We discuss Lepp-centroid versus Lepp-midpoint algorithms for Delaunay quality triangulation. We present geometrical results that ensure that the centroid version produces triangulations with both average smallest angles greater than those obtained with the midpoint version and with bigger smallest edges, without suffering from a rare looping case associated to the midpoint method. Empirical study shows that the centroid method behaves significantly better than the midpoint version (and than the offcenter algorithm for angles bigger than 25 ), for geometries whose initial Delaunay triangulation have triangle smallest edges over the boundary.This research was supported by DI ENL 07/03. We are grateful to Bruce Simpson who contributed to an early formulation of this paper