Algorithms for Delaunay Triangulation

Abstract

Several algorithms have been developed for Delaunay triangulation based on the definitions and the theory of the previous chapter. The popularity of the Delaunay triangulation is twofold. It yields “good shaped” triangles (in the plane) and the theory, mainly based on its dual, the Voronoi diagram, is well established. Other types of triangulation, such as triangulations that are optimal in the sense of the MinMax angle criterion, are difficult to compute in reasonable time from a large number of points. In fact, the Delaunay swapping criteria, which were shown to be equivalent in Section 3.6, are the only known criteria that can be used in Lawson’s local optimization procedure (LOP) to guarantee a globally optimal triangulation.