swMATH ID: 118
Software Authors: CGAL Editorial Board
Description: The goal of the CGAL Open Source Project is to provide easy access to efficient and reliable geometric algorithms in the form of a C++ library. CGAL is used in various areas needing geometric computation, such as: computer graphics, scientific visualization, computer aided design and modeling, geographic information systems, molecular biology, medical imaging, robotics and motion planning, mesh generation, numerical methods... More on the projects using CGAL web page. The Computational Geometry Algorithms Library (CGAL), offers data structures and algorithms like triangulations (2D constrained triangulations and Delaunay triangulations in 2D and 3D, periodic triangulations in 3D), Voronoi diagrams (for 2D and 3D points, 2D additively weighted Voronoi diagrams, and segment Voronoi diagrams), polygons (Boolean operations, offsets, straight skeleton), polyhedra (Boolean operations), arrangements of curves and their applications (2D and 3D envelopes, Minkowski sums), mesh generation (2D Delaunay mesh generation and 3D surface and volume mesh generation, skin surfaces), geometry processing (surface mesh simplification, subdivision and parameterization, as well as estimation of local differential properties, and approximation of ridges and umbilics), alpha shapes, convex hull algorithms (in 2D, 3D and dD), search structures (kd trees for nearest neighbor search, and range and segment trees), interpolation (natural neighbor interpolation and placement of streamlines), shape analysis, fitting, and distances (smallest enclosing sphere of points or spheres, smallest enclosing ellipsoid of points, principal component analysis), and kinetic data structures. All these data structures and algorithms operate on geometric objects like points and segments, and perform geometric tests on them. These objects and predicates are regrouped in CGAL Kernels. Finally, the Support Library offers geometric object generators and spatial sorting functions, as well as a matrix search framework and a solver for linear and quadratic programs. It further offers interfaces to third party software such as the GUI libraries Qt, Geomview, and the Boost Graph Library.
Homepage: http://www.cgal.org/
Programming Languages: C++
Operating Systems: Linux, Mac OS, Windows
Dependencies: GMP, MPFR, LEDA, RS, RS3, NTL, Eigen, libQGLViewer, Coin3D, ESBTL, Intel TBB, Qt4
Keywords: orms; computational geometry; software library; C++; generic programming
Related Software: LEDA; 2D triangulations; Triangle; 2D Arrangement; Boost; TetGen; Gmsh; Qhull; Boost C++ Libraries; GitHub; Powercrust; EXACUS; Eigen; gmp; Traits; BGL; deal.ii; Python; VTK; CutFEM
Cited in: 417 Documents
This software is also referenced in ORMS.
Further Publications: http://www.cgal.org/Manual/3.2/doc_html/cgal_manual/biblio.html
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Cited by 878 Authors

24 Halperin, Dan
15 Teillaud, Monique
14 Fogel, Efi
13 Berberich, Eric
12 Mehlhorn, Kurt
10 Pion, Sylvain
10 Wein, Ron
10 Yap, Chee-Keng
9 Boissonnat, Jean-Daniel
9 Devillers, Olivier
9 Hemmer, Michael
9 Sagraloff, Michael
8 Kettner, Lutz
6 Emiris, Ioannis Z.
6 Fisikopoulos, Vissarion
6 Kerber, Michael
6 Yvinec, Mariette
5 Alliez, Pierre
5 Hert, Susan
5 Lazard, Sylvain
5 Mérigot, Quentin
5 Peñaranda, Luis Mariano
4 Cazals, Frédéric
4 Chernikov, Andrey N.
4 Chrisochoides, Nikos P.
4 Emeliyanenko, Pavel
4 Hachenberger, Peter
4 Hiraoka, Yasuaki
4 Näher, Stefan
4 Schirra, Stefan
4 Schömer, Elmar
4 Sharir, Micha
4 Snoeyink, Jack Scott
4 Wachsmuth, Gerd
3 Agarwal, Pankaj Kumar
3 Caroli, Manuel
3 Casas, Eduardo
3 Chiang, Yi-Jen
3 De Castro, Pedro Machado Manhães
3 de Gournay, Frédéric
3 de Rezende, Pedro Jussieu
3 de Souza, Cid Carvalho
3 Duque, Daniel
3 Eigenwillig, Arno
3 Elber, Gershon
3 Everett, Hazel
3 Feder, Marco
3 Flato, Eyal
3 Gärtner, Bernd
3 Hanniel, Iddo
3 Heltai, Luca
3 Herzog, Roland
3 Hoffmann, Michael
3 Kahn, Jonas
3 Kim, Deok-Soo
3 Kobel, Alexander
3 Lebrat, Léo
3 Loriot, Sebastien
3 Lucet, Yves
3 Milenkovic, Victor J.
3 Millman, David L.
3 Munch, Peter
3 Muthuganapathy, Ramanathan
3 Preisig, Matthias
3 Sacks, Elisha P.
3 Seel, Michael
3 Selberherr, Siegfried
3 Setter, Ophir
3 Thibert, Boris
3 Tsigaridas, Elias P.
3 Wagner, Dorothea
3 Wei, Huayi
2 Antonietti, Paola Francesca
2 Arndt, Daniel
2 Bangerth, Wolfgang
2 Baram, Alon
2 Batista, Vicente H. F.
2 Boman, Romain C.
2 Brazil, Marcus N.
2 Brönnimann, Hervé
2 Burbulla, Samuel
2 Butt, Nabeel
2 Chazal, Frédéric
2 Chen, Long
2 Cheng, Ho-Lun
2 Cheng, Jinsan
2 Cohen-Steiner, David
2 Damiand, Guillaume
2 Dedner, Andreas S.
2 Delage, Christophe
2 Demetrescu, Camil
2 Du, Zilin
2 Duarte, Carlos Armando
2 Dufourd, Jean-François
2 Dupont, Florent
2 Edelsbrunner, Herbert
2 Eder, Günther
2 Español, Pep
2 Ezra, Eti
2 Fehling, Marc
...and 778 more Authors
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Cited in 116 Serials

39 Computational Geometry
23 Computer Aided Geometric Design
16 Computer Methods in Applied Mechanics and Engineering
15 Journal of Computational Physics
11 Discrete & Computational Geometry
11 International Journal of Computational Geometry & Applications
11 SIAM Journal on Scientific Computing
10 International Journal for Numerical Methods in Engineering
7 Computers & Mathematics with Applications
7 ACM Transactions on Mathematical Software
6 Numerische Mathematik
6 Theoretical Computer Science
5 Journal of Computational and Applied Mathematics
5 Journal of Mathematical Imaging and Vision
4 Computers and Fluids
4 Algorithmica
4 Mathematics in Computer Science
4 SIAM Journal on Imaging Sciences
3 Information Processing Letters
3 Applied Mathematics and Computation
3 SIAM Journal on Numerical Analysis
3 Computational Mechanics
3 CAD. Computer-Aided Design
3 Journal of Global Optimization
3 Computational Optimization and Applications
3 Computational Geosciences
2 Computer Physics Communications
2 Science of Computer Programming
2 ACM Transactions on Graphics
2 Computers & Operations Research
2 Journal of Scientific Computing
2 Japan Journal of Industrial and Applied Mathematics
2 European Journal of Operational Research
2 Mathematical Programming. Series A. Series B
2 Journal of Numerical Mathematics
2 ACM Journal of Experimental Algorithmics
2 Communications in Computational Physics
2 ACM Communications in Computer Algebra
2 Algorithms
2 Mathematics and Visualization
2 Discrete Mathematics and its Applications
1 Advances in Applied Probability
1 Discrete Applied Mathematics
1 Journal of Mathematical Biology
1 Molecular Simulation
1 Mathematics of Computation
1 Bulletin of Mathematical Biology
1 Fortschritte der Physik
1 Advances in Mathematics
1 Computing
1 International Journal of Game Theory
1 Journal of Multivariate Analysis
1 Journal of Optimization Theory and Applications
1 Mathematics and Computers in Simulation
1 Networks
1 SIAM Journal on Computing
1 Software. Practice & Experience
1 International Journal of Production Research
1 Applied Numerical Mathematics
1 Journal of Symbolic Computation
1 Journal of Complexity
1 Constructive Approximation
1 Journal of Economic Dynamics & Control
1 Discrete Event Dynamic Systems
1 Numerical Algorithms
1 Computational Statistics
1 Applied Mathematical Modelling
1 Doklady Bolgarskoĭ Akademii Nauk
1 Pattern Recognition
1 SIAM Journal on Applied Mathematics
1 SIAM Journal on Mathematical Analysis
1 SIAM Journal on Optimization
1 Advances in Engineering Software
1 Applied Mathematics. Series B (English Edition)
1 International Journal of Computer Vision
1 Computational and Applied Mathematics
1 Advances in Applied Clifford Algebras
1 Russian Journal of Numerical Analysis and Mathematical Modelling
1 Advances in Computational Mathematics
1 The Journal of Artificial Intelligence Research (JAIR)
1 Documenta Mathematica
1 INFORMS Journal on Computing
1 Mathematical Methods of Operations Research
1 Journal of Graph Algorithms and Applications
1 European Journal of Mechanics. B. Fluids
1 International Journal of Applied Mathematics and Computer Science
1 Optimization and Engineering
1 Graphical Models
1 The Journal of Logic and Algebraic Programming
1 Foundations of Computational Mathematics
1 Journal of Machine Learning Research (JMLR)
1 ASTIN Bulletin
1 International Journal of Computational Methods
1 Journal of Statistical Mechanics: Theory and Experiment
1 International Journal of Parallel, Emergent and Distributed Systems
1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis
1 The European Physical Journal C. Particles and Fields
1 Lecture Notes in Computer Science
1 Mathematical Surveys and Monographs
...and 16 more Serials
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Cited in 46 Fields

202 Numerical analysis (65-XX)
198 Computer science (68-XX)
43 Convex and discrete geometry (52-XX)
33 Operations research, mathematical programming (90-XX)
32 Mechanics of deformable solids (74-XX)
31 Fluid mechanics (76-XX)
27 Partial differential equations (35-XX)
26 Biology and other natural sciences (92-XX)
15 Algebraic geometry (14-XX)
14 Combinatorics (05-XX)
14 Calculus of variations and optimal control; optimization (49-XX)
10 Statistics (62-XX)
10 Information and communication theory, circuits (94-XX)
8 Probability theory and stochastic processes (60-XX)
7 Geometry (51-XX)
6 Algebraic topology (55-XX)
6 Game theory, economics, finance, and other social and behavioral sciences (91-XX)
5 Differential geometry (53-XX)
5 Mechanics of particles and systems (70-XX)
5 Statistical mechanics, structure of matter (82-XX)
5 Geophysics (86-XX)
4 General and overarching topics; collections (00-XX)
3 Mathematical logic and foundations (03-XX)
3 Number theory (11-XX)
3 Approximations and expansions (41-XX)
3 Manifolds and cell complexes (57-XX)
3 Optics, electromagnetic theory (78-XX)
3 Quantum theory (81-XX)
2 Real functions (26-XX)
2 General topology (54-XX)
2 Global analysis, analysis on manifolds (58-XX)
2 Classical thermodynamics, heat transfer (80-XX)
2 Astronomy and astrophysics (85-XX)
2 Systems theory; control (93-XX)
1 Commutative algebra (13-XX)
1 Linear and multilinear algebra; matrix theory (15-XX)
1 Associative rings and algebras (16-XX)
1 Group theory and generalizations (20-XX)
1 Measure and integration (28-XX)
1 Functions of a complex variable (30-XX)
1 Several complex variables and analytic spaces (32-XX)
1 Dynamical systems and ergodic theory (37-XX)
1 Integral transforms, operational calculus (44-XX)
1 Integral equations (45-XX)
1 Functional analysis (46-XX)
1 Operator theory (47-XX)

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