ACS Algorithms for Complex Shapes with Certified Numerics and Topology FPG: A code generator for fast and certified geometric predicates

FPG: A code generator for fast and certified geometric predicates

We present a general purpose code analyzer and generator for filtered predicates, which are critical for geometric algorithms. While there already exist such code generators, our contribution is to generate ”almost static filters”, a type of filter which could not be generated previously. The generated and safe filtered predicates are almost as fast as their inexact floating point counterparts,...

ACS Algorithms for Complex Shapes with Certified Numerics and Topology Application of algebraic tools to CSG operations on curves and surfaces

ACS Algorithms for Complex Shapes with Certified Numerics and Topology Computation of the medial axis of smooth curves with topological guarantees

Project co-funded by the European Commission within FP6 (2002–2006) under contract nr. IST-006413

ACS Algorithms for Complex Shapes with Certified Numerics and Topology Anisotropic mesh generation

Project co-funded by the European Commission within FP6 (2002–2006) under contract nr. IST-006413

ACS Algorithms for Complex Shapes with Certified Numerics and Topology Algebraic tools for the Voronoi diagram of ellipses, leading to an experimental implementation

We study the four predicates required for the Voronoi diagram of ellipses in the plane, under the Euclidean metric, based on an incremental algorithm. The report concentrates on InCircle, which is the hardest predicate: it decides the position of a query ellipse relative to the Voronoi circle of three given ellipses. The implementation of InCircle combines a certified numeric algorithm with alg...