CGAL swMATH ID: 118 Software Authors: Board, CGAL Editorial 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; GitHub; Boost C++ Libraries; Powercrust; EXACUS; Eigen; deal.ii; Python; gmp; Traits; CPLEX; VTK; BGL Cited in: 445 Documents This software is also referenced in ORMS. Further Publications: http://www.cgal.org/Manual/3.2/doc_html/cgal_manual/biblio.html Standard Articles 4 Publications describing the Software, including 4 Publications in zbMATH Year CGAL – reliable geometric computing for academia and industry. Zbl 1434.65008Berberich, Eric 2014 CGAL Arrangements and their applications. A step-by-step guide. Zbl 1258.65025Fogel, Efi; Halperin, Dan; Wein, Ron 2012 Exact geometric and algebraic computations in CGAL. Zbl 1274.65060Karavelas, Menelaos I. 2010 On the design of CGAL a computational geometry algorithms library. Zbl 1147.68781Fabri, Andreas; Giezeman, Geert-Jan; Kettner, Lutz; Schirra, Stefan; Schönherr, Sven 2000 all top 5 Cited by 943 Authors 31 Halperin, Dan 16 Teillaud, Monique 14 Fogel, Efi 13 Berberich, Eric 12 Mehlhorn, Kurt 10 Hemmer, Michael 10 Pion, Sylvain 10 Wein, Ron 10 Yap, Chee-Keng 9 Boissonnat, Jean-Daniel 9 Devillers, Olivier 9 Sagraloff, Michael 8 Kettner, Lutz 6 Emiris, Ioannis Z. 6 Fisikopoulos, Vissarion 6 Kerber, Michael 6 Mérigot, Quentin 6 Yvinec, Mariette 5 Alliez, Pierre 5 Hert, Susan 5 Lazard, Sylvain 5 Peñaranda, Luis Mariano 4 Cazals, Frédéric 4 Chernikov, Andrey N. 4 Chrisochoides, Nikos P. 4 de Rezende, Pedro Jussieu 4 de Souza, Cid Carvalho 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 Antonietti, Paola Francesca 3 Boman, Romain C. 3 Caroli, Manuel 3 Casas, Eduardo 3 Chiang, Yi-Jen 3 De Castro, Pedro Machado Manhães 3 de Gournay, Frédéric 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 Held, Martin 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 Ponthot, Jean-Philippe 3 Preisig, Matthias 3 Rohde, Christian 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 3 Yan, Dongming 2 Arndt, Daniel 2 Bangerth, Wolfgang 2 Baram, Alon 2 Batista, Vicente H. F. 2 Bordas, Stéphane Pierre Alain 2 Brazil, Marcus N. 2 Brönnimann, Hervé 2 Burbulla, Samuel 2 Butt, Nabeel 2 Calvin, James M. 2 Chareyre, Bruno 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 ...and 843 more Authors all top 5 Cited in 120 Serials 40 Computational Geometry 24 Computer Aided Geometric Design 17 Computer Methods in Applied Mechanics and Engineering 17 International Journal for Numerical Methods in Engineering 15 Journal of Computational Physics 12 Discrete & Computational Geometry 12 International Journal of Computational Geometry & Applications 12 SIAM Journal on Scientific Computing 9 Computers & Mathematics with Applications 9 ACM Transactions on Mathematical Software 6 Numerische Mathematik 6 Theoretical Computer Science 5 Computers and Fluids 5 Journal of Computational and Applied Mathematics 5 Journal of Mathematical Imaging and Vision 4 Computer Physics Communications 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. 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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 International Transactions in Operational Research 1 Documenta Mathematica 1 INFORMS Journal on Computing 1 Mathematical Methods of Operations Research 1 Journal of Graph Algorithms and Applications 1 Journal of the ACM 1 Discrete Mathematics and Theoretical Computer Science. DMTCS 1 European Journal of Mechanics. B. Fluids 1 International Journal of Applied Mathematics and Computer Science 1 Optimization and Engineering 1 Lobachevskii Journal of Mathematics 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 ...and 20 more Serials all top 5 Cited in 47 Fields 213 Numerical analysis (65-XX) 209 Computer science (68-XX) 45 Convex and discrete geometry (52-XX) 37 Mechanics of deformable solids (74-XX) 35 Fluid mechanics (76-XX) 34 Operations research, mathematical programming (90-XX) 30 Partial differential equations (35-XX) 26 Biology and other natural sciences (92-XX) 16 Algebraic geometry (14-XX) 15 Combinatorics (05-XX) 14 Calculus of variations and optimal control; optimization (49-XX) 10 Statistics (62-XX) 8 Probability theory and stochastic processes (60-XX) 7 Geometry (51-XX) 7 Information and communication theory, circuits (94-XX) 6 Algebraic topology (55-XX) 6 Statistical mechanics, structure of matter (82-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Differential geometry (53-XX) 5 Manifolds and cell complexes (57-XX) 5 Mechanics of particles and systems (70-XX) 5 Geophysics (86-XX) 4 General and overarching topics; collections (00-XX) 4 Approximations and expansions (41-XX) 3 Mathematical logic and foundations (03-XX) 3 Number theory (11-XX) 3 Global analysis, analysis on manifolds (58-XX) 3 Optics, electromagnetic theory (78-XX) 3 Systems theory; control (93-XX) 2 Real functions (26-XX) 2 Several complex variables and analytic spaces (32-XX) 2 General topology (54-XX) 2 Classical thermodynamics, heat transfer (80-XX) 2 Quantum theory (81-XX) 2 Astronomy and astrophysics (85-XX) 1 Order, lattices, ordered algebraic structures (06-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 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) Citations by Year