Introduction to Solid Modeling
Introduction to Solid Modeling
Geometric and solid modeling: an introduction
Geometric and solid modeling: an introduction
Introduction to algorithms
Oriented projective geometry
A rational rotation method for robust geometric algorithms
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Towards exact geometric computation
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
Using generic programming for designing a data structure for polyhedral surfaces
Computational Geometry: Theory and Applications - Special issue on applications and challenges
LEDA: a platform for combinatorial and geometric computing
LEDA: a platform for combinatorial and geometric computing
On the design of CGAL a computational geometry algorithms library
Software—Practice & Experience - Special issue on discrete algorithm engineering
A Complete and Efficient Algorithm for the Intersection of a General and a Convex Polyhedron
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Computational Geometry: Theory and Applications
Contributing vertices-based Minkowski sum computation of convex polyhedra
Computer-Aided Design
SGP '09 Proceedings of the Symposium on Geometry Processing
An implicit complexes framework for heterogeneous objects modelling
Heterogeneous objects modelling and applications
Industrial application of exact Boolean operations for meshes
Proceedings of the 26th Spring Conference on Computer Graphics
Fast and robust generation of city-scale seamless 3D urban models
Computer-Aided Design
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Nef polyhedra in d-dimensional space are the closure of half-spaces under boolean set operation. In consequence, they can represent non-manifold situations, open and closed sets, mixed-dimensional complexes and they are closed under all boolean and topological operations, such as complement and boundary. They were introduced by W. Nef in his seminal 1978 book on polyhedra.We presented in previous work a new data structure for the boundary representation of three-dimensional Nef polyhedra with efficient algorithms for boolean operations. These algorithms were designed for correctness and can handle all cases, in particular all degeneracies. To this extent we rely on exact arithmetic to avoid well known problems with floating-point arithmetic.In this paper, we present important optimizations for the algorithms. We describe the chosen implementations for the point-location and the intersection-finding subroutines, a kd-tree and a fast box-intersection algorithm, respectively. We evaluate this optimized implementation with extensive experiments that supplement the runtime analysis from our previous paper and that illustrate the effectiveness of our optimizations. We compare our implementation with the ACIS CAD kernel and demonstrate the power and cost of the exact arithmetic in near-degenerate situations.The implementation was released as Open Source in the CGAL release 3.1 in December 2004.