Algorithms for Complex Shapes with Certified Numerics and Topology Computing Envelopes of Quadrics

ACS Algorithms for Complex Shapes with Certified Numerics and Topology Evaluation of different approaches in 3D curved kernel for arrangements of quadrics

Within the context of the ACS project we have investigated two approaches towards the arrangements of quadrics. The first approach, which is presented in ACS-TR-241402-01, computes the adjacency graph of the arrangement and is based on an exact parameterization of the appearing intersection curves. The second approach, which is presented in ACS-TR-241402-02, computes the arrangement on each qua...

Algorithms for Complex Shapes with Certified Numerics and Topology Constructing Two-Dimensional Voronoi Diagrams via Divide-and-Conquer of Envelopes in Space

We present a general framework for computing two-dimensional Voronoi diagrams of different site classes under various distance functions. The computation of the diagrams employs the cgal software for constructing envelopes of surfaces in 3-space, which implements a divide-and-conquer algorithm. A straightforward application of the divide-and-conquer approach for Voronoi diagrams yields highly i...

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 Exact and Efficient Construction of Planar Arrangements of Circular Arcs and Line Segments with Applications

We describe a simple yet powerful approach for computing planar arrangements of circular arcs and line segments in a robust and exact manner. Constructing arrangements using this approach is about one order of magnitude faster compared to other techniques that employ the exact computation paradigm. We have successfully applied our technique for computing offsets of planar polygons and for perfo...

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