A Time Efficient Delaunay Refinement Algorithm

In this paper we present a Delaunay refinement algorithm for generating good aspect ratio and optimal size triangulations. This is the first algorithm known to have sub-quadratic running time. The algorithm is based on the extremely popular Delaunay refinement algorithm of Ruppert. We know of no prior refinement algorithm with an analyzed subquadratic time bound. For many natural classes of meshing problems, our time bounds are comparable to know bounds for quadtree methods.