Computational geometry: an introduction
Computational geometry: an introduction
Sweeping arrangements of curves
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
A fast planar partition algorithm, I
Journal of Symbolic Computation
Design patterns: elements of reusable object-oriented software
Design patterns: elements of reusable object-oriented software
Generic programming and the STL: using and extending the C++ Standard Template Library
Generic programming and the STL: using and extending the C++ Standard Template Library
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
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
Triangulations in CGAL (extended abstract)
Proceedings of the sixteenth annual symposium on Computational geometry
On the design of CGAL a computational geometry algorithms library
Software—Practice & Experience - Special issue on discrete algorithm engineering
Interval arithmetic yields efficient dynamic filters for computational geometry
Discrete Applied Mathematics - Special issue 14th European workshop on computational geometry CG'98 Selected papers
The design and implementation of panar maps in CGAL
Journal of Experimental Algorithmics (JEA)
The boost graph library: user guide and reference manual
The boost graph library: user guide and reference manual
Polygon decomposition for efficient construction of Minkowski sums
Computational Geometry: Theory and Applications - Special issue on: Sixteenth European Workshop on Computational Geometry (EUROCG-2000)
High-Level Filtering for Arrangements of Conic Arcs
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
A Computational Basis for Conic Arcs and Boolean Operations on Conic Polygons
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Complete, exact, and efficient computations with cubic curves
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Towards and open curved kernel
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
The visibility-Voronoi complex and its applications
Computational Geometry: Theory and Applications - Special issue on the 21st European workshop on computational geometry (EWCG 2005)
Robust, generic and efficient construction of envelopes of surfaces in three-dimensional spaces
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
EXACUS: efficient and exact algorithms for curves and surfaces
ESA'05 Proceedings of the 13th annual European conference on Algorithms
An exact, complete and efficient computation of arrangements of Bézier curves
Proceedings of the 2007 ACM symposium on Solid and physical modeling
Computing the Voronoi cells of planes, spheres and cylinders in R3
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Proceedings of the 2008 ACM symposium on Solid and physical modeling
The complexity of the outer face in arrangements of random segments
Proceedings of the twenty-fourth annual symposium on Computational geometry
Exact geometric-topological analysis of algebraic surfaces
Proceedings of the twenty-fourth annual symposium on Computational geometry
Arrangements of geodesic arcs on the sphere
Proceedings of the twenty-fourth annual symposium on Computational geometry
An experimental study of point location in planar arrangements in CGAL
Journal of Experimental Algorithmics (JEA)
Computing the arrangement of circles on a sphere, with applications in structural biology
Computational Geometry: Theory and Applications
Computer Aided Geometric Design
An efficient algorithm for the stratification and triangulation of an algebraic surface
Computational Geometry: Theory and Applications
Sweeping and maintaining two-dimensional arrangements on surfaces: a first step
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Fast and robust retrieval of Minkowski sums of rotating convex polyhedra in 3-space
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Optimizing the layout of proportional symbol maps
ICCSA'11 Proceedings of the 2011 international conference on Computational science and its applications - Volume Part III
Fast and robust retrieval of Minkowski sums of rotating convex polyhedra in 3-space
Computer-Aided Design
Lines through segments in 3d space
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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Arrangements of planar curves are fundamental structures in computational geometry. Recently, the arrangement package of Cgal, the Computational Geometry Algorithms Library, has been redesigned and re-implemented exploiting several advanced programming techniques. The resulting software package, which constructs and maintains planar arrangements, is easier to use, to extend, and to adapt to a variety of applications. It is more efficient space- and time-wise, and more robust. The implementation is complete in the sense that it handles degenerate input, and it produces exact results. In this paper we describe how various programming techniques were used to accomplish specific tasks within the context of computational geometry in general and arrangements in particular. These tasks are exemplified by several applications, whose robust implementation is based on the arrangement package. Together with a set of benchmarks they assured the successful application of the various programming techniques.