A Delaunay Refinement Algorithm for Quality 2-Dimensional Mesh Generation

Abstract

We present a simple new algorithm for triangulating polygons and planar straightline graphs, It provides "shape" and "size" guarantees: •All triangles have a bounded aspect ratio.•The number of triangles is within a constant factor of optimal. Such "quality" triangulations are desirable as meshes for the finite element method, in which the running time generally increases with the number of triangles, and where the convergence and stability may be hurt by very skinny triangles. The technique we use-successive refinement of a Delaunay triangulation-extends a mesh generation technique of Chew by allowing triangles of varying sizes. Compared with previous quadtree-based algorithms for quality mesh generation, the Delaunay refinement approach is much simpler and generally produces meshes with fewer triangles. We also discuss an implementation of the algorithm and evaluate its performance on a variety of inputs.