Triangulations with locally optimal Steiner points

We present two new Delaunay refinement algorithms, second an extension of the first. For a given input domain (a set of points or a planar straight line graph), and a threshold angle , the Delaunay refinement algorithms compute triangulations that have all angles at least . 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 20.7 . In practice, it generally works for 34 and fails to terminate for larger constraint angles. The new variant of the Delaunay refinement algorithm generally terminates for constraint angles up to 42 . Experiments also indicate that our algorithm computes significantly (almost by a factor of two) smaller triangulations than the output of the previous Delaunay refinement algorithms. Categories and Subject Descriptors (according to ACM CCS): F.2.2 [Nonnumerical Algorithms and Problems]: Geom...

• Type: Conference
• Year: 2007
• Where: SGP
• Authors: Hale Erten, Alper Üngör
• Keywords: Algorithms Compute Triangulations, Computer Graphics, Delaunay Refinement Algorithms, Original Delaunay Refinement, SGP 2007