Triangle Mesh Generation: Delaunay Triangulation

Abstract

In this chapter, the generation of triangle meshes from points is illustrated via the Delaunay triangulation. Apart from Delaunay triangulation being the most common triangulation method, the aim is also to give an overview of the typical issues of point triangulation in general. As such the aspects of numerical accuracy and constraint triangulation are also covered. Central constructive proofs of Delaunay triangulation are covered along with the connection to Voronoi diagrams and convex hulls. The aim is that the student should be able to complete an exercise in performing Delaunay triangulation after this chapter; as such the flip algorithm is covered in some detail, as well as the geometric primitives in circle and left of. These primitives are the foundation of many triangulation algorithms. The arguably most efficient algorithm for 2D Delaunay triangulation, the divide and conquer algorithm, is also presented.