Introduction to Solid Modeling
Introduction to Solid Modeling
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
Static analysis yields efficient exact integer arithmetic for computational geometry
ACM Transactions on Graphics (TOG)
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
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
MAPC: a library for efficient and exact manipulation of algebraic points and curves
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
On the design of CGAL a computational geometry algorithms library
Software—Practice & Experience - Special issue on discrete algorithm engineering
Implementing Geometric Algorithms Robustly
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
The CGAL Kernel: A Basis for Geometric Computation
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Exact minkowski sums and applications
Proceedings of the eighteenth annual symposium on Computational geometry
Improved construction of vertical decompositions of three-dimensional arrangements
Proceedings of the eighteenth annual symposium on Computational geometry
Polygon decomposition for efficient construction of Minkowski sums
Computational Geometry: Theory and Applications - Special issue on: Sixteenth European Workshop on Computational Geometry (EUROCG-2000)
Speeding Up the Incremental Construction of the Union of Geometric Objects in Practice
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Continuous path verification in multi-axis NC-machining
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Complete, exact, and efficient computations with cubic curves
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
An approximate arrangement algorithm for semi-algebraic curves
Proceedings of the twenty-second annual symposium on Computational geometry
Exact, efficient, and complete arrangement computation for cubic curves
Computational Geometry: Theory and Applications
Computer-Aided Design
Proceedings of the 2007 ACM symposium on Applied computing
Advanced programming techniques applied to Cgal's arrangement package
Computational Geometry: Theory and Applications
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
Clip Art Rendering of Smooth Isosurfaces
IEEE Transactions on Visualization and Computer Graphics
The visual hull of piecewise smooth objects
Computer Vision and Image Understanding
The complexity of the outer face in arrangements of random segments
Proceedings of the twenty-fourth annual symposium on Computational geometry
Polyhedra genus theorem and Euler formula: A hypermap-formalized intuitionistic proof
Theoretical Computer Science
Improving the topology computation of an arrangement of cubics
Computational Geometry: Theory and Applications
Exact, efficient, and complete arrangement computation for cubic curves
Computational Geometry: Theory and Applications
Precise global collision detection in multi-axis NC-machining
Computer-Aided Design
Computing the topology of an arrangement of quartics
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
Journal of Symbolic Computation
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Non-Photorealistic Animation and Rendering
EXACUS: efficient and exact algorithms for curves and surfaces
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Improved implementation of point location in general two-dimensional subdivisions
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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Planar maps are fundamental structures in computational geometry. They are used to represent the subdivision of the plane into regions and have numerous applications. We describe the planar map package of CGAL--a Computational Geometry Algorithms Library. We discuss its modular design and implementation. In particular we introduce the two main classes of the design--planar maps and topological maps that enable the convenient separation between geometry and topology. The modular design is implemented using a generic programming approach. By switching a template parameter--the geometric traits class, one can use the same code for planar maps of different objects such as line segments or circular arcs. More flexibility is achieved by choosing a point location algorithm out of three implemented algorithms or plugging in an algorithm implemented by the user. The user of the planar maps package can benefit both from its flexibility and robustness. We present several examples of geometric traits classes and point location algorithms which demonstrate the possibility to adapt the general package to specific needs.