Algorithms for Complex Shapes with Certified Numerics and Topology Arrangements of Geodesic Arcs on the Sphere

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 An Experimental Study of Point Location in General Planar Arrangements

We study the performance in practice of various point-location algorithms implemented in cgal, including a newly devised Landmarks algorithm. Among the other algorithms studied are: a näıve approach, a “walk along a line” strategy and a trapezoidal-decomposition based search structure. The current implementation addresses general arrangements of arbitrary planar curves, including arrangements o...

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

Exact Implementation of Arrangements of Geodesic Arcs on the Sphere with Applications

Recently, the Arrangement 2 package of Cgal, the Computational Geometry Algorithms Library, has been greatly extended to support arrangements of curves embedded on two-dimensional parametric surfaces. The general framework for sweeping a set of curves embedded on a two-dimensional parametric surface was introduced in [3]. In this paper we concentrate on the specific algorithms and implementatio...

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...