ABSTRACT
Delaunay refinement algorithms generate high-quality meshes by inserting vertices into a Delaunay or constrained Delaunay triangulation. The vertices are placed to ensure domain conformity and to eliminate elements that are badly shaped or too large. Delaunay refinement has many virtues: the optimality of Delaunay triangulations with respect to criteria related to interpolation and the smallest angles; our rich inheritance of theory and algorithms for Delaunay triangulations; the fast, local nature of vertex insertion; and most importantly, the guidance that the Delaunay triangulation provides in finding locations to place new vertices that are far from the other vertices, so that short edges do not appear.
