Erten, HaleUengoer, AlperAlexander Belyaev and Michael Garland2014-01-292014-01-292007978-3-905673-46-31727-8384https://doi.org/10.2312/SGP/SGP07/143-152We present two new Delaunay refinement algorithms, the second an extension of the first. For a given input domain (a set of points in the plane or a planar straight line graph), and a threshold angle a, the Delaunay refinement algorithms compute triangulations that have all angles at least a. Our algorithms have the same theoretical guarantees as the previous Delaunay refinement algorithms. The original Delaunay refinement algorithm of Ruppert is proven to terminate with size-optimal quality triangulations for aCategories and Subject Descriptors (according to ACM CCS): F.2.2 [Nonnumerical Algorithms and Problems]: Geometrical problems and computations I.3.5 [Computational Geometry and Object Modeling]: Geometric algorithms, languages, and systems