Efficient Exact Geometric Predicates for Delaunay Triangulations

摘要

A time efficient implementation of the exact geometric computation paradigm relies on arithmetic filters which are used to speed up the exact computation of easy instances of the geometric predicates. Depending of what is called "easy instances", we usually classify filters as static or dynamic and also some in between categories often called semi-static. In this paper, we propose, in the context of three dimensional Delaunay triangulations: 1. automatic tools for the writing of static and semi-static filters, 2. a new semi-static level of filtering called translation filter, 3. detailed benchmarks of the success rates of these filters and comparison with rounded arithmetic, long integer arithmetic and filters provided in Shewchuk's predicates. Our method is general and can be applied to all geometric predicates on points that can be expressed as signs of polynomial expressions. This work is applied in the CGAL library.