O.-Centers: A New Type of Steiner Points for Computing Size-Optimal Quality-Guaranteed Delaunay Triangulations

We introduce a new type of Steiner points, called off-centers, as an alternative to circumcenters, to improve the quality of Delaunay triangulations. We propose a new Delaunay refinement algorithm based on iterative insertion of off-centers. We show that this new algorithm has the same quality and size optimality guarantees of the best known refinement algorithms. In practice, however, the new algorithm inserts about 40% fewer Steiner points (hence runs faster) and generates triangulations that have about 30% fewer elements compared with the best previous algorithms.