The Delaunay triangulation by grid subdivision

Abstract

This study presents an efficient algorithm of Delaunay triangulation by grid subdivision. The proposed algorithm show a superior performance in terms of execution time to the incremental algorithm and uniform grid method mainly due to the efficient way of searching a mate. In the proposed algorithm, uniform grids are divided into sub-grids depending on the density of points and areas with high chance of finding a mate is explored first. Most of the previous researches have focused on theoretical aspects of the triangulation, but this study presents empirical results of computer implementation in 2-dimension and 3-dimension, respectively. © Springer-Verlag Berlin Heidelberg 2005.