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.

This software is also referenced in ORMS.

References in zbMATH (referenced in 226 articles , 4 standard articles )

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  1. Elliott, Charles M.; Ranner, Thomas; Venkataraman, Chandrasekhar: Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics (2017)
  2. Ernestus, Maximilian; Friedrichs, Stephan; Hemmer, Michael; Kokemüller, Jan; Kröller, Alexander; Moeini, Mahdi; Schmidt, Christiane: Algorithms for art gallery illumination (2017)
  3. Ibanez, Dan; Shephard, Mark S.: Modifiable array data structures for mesh topology (2017)
  4. Simon, K.; Sheorey, S.; Jacobs, D.W.; Basri, R.: A hyperelastic two-scale optimization model for shape matching (2017)
  5. Antonietti, Paola F.; Formaggia, Luca; Scotti, Anna; Verani, Marco; Verzott, Nicola: Mimetic finite difference approximation of flows in fractured porous media (2016)
  6. Benamou, Jean-David; Carlier, Guillaume; Mérigot, Quentin; Oudet, Édouard: Discretization of functionals involving the Monge-Ampère operator (2016)
  7. Buchet, Mickaël; Chazal, Frédéric; Oudot, Steve Y.; Sheehy, Donald R.: Efficient and robust persistent homology for measures (2016)
  8. Caroli, Manuel; Teillaud, Monique: Delaunay triangulations of closed Euclidean $d$-orbifolds (2016)
  9. Dedner, Andreas; Madhavan, Pravin: Adaptive discontinuous Galerkin methods on surfaces (2016)
  10. Escolar, Emerson G.; Hiraoka, Yasuaki: Persistence modules on commutative ladders of finite type (2016)
  11. Fisikopoulos, Vissarion; Peñaranda, Luis: Faster geometric algorithms via dynamic determinant computation (2016)
  12. Hemmer, Michael; Kleinbort, Michal; Halperin, Dan: Optimal randomized incremental construction for guaranteed logarithmic planar point location (2016)
  13. Joulaian, Meysam; Hubrich, Simeon; Düster, Alexander: Numerical integration of discontinuities on arbitrary domains based on moment Fitting (2016)
  14. Lee, Mokwon; Sugihara, Kokichi; Kim, Deok-Soo: Topology-oriented incremental algorithm for the robust construction of the Voronoi diagrams of disks (2016)
  15. Machado Manhães de Castro, Pedro; Mérigot, Quentin; Thibert, Boris: Far-field reflector problem and intersection of paraboloids (2016)
  16. Peterka, Tom; Croubois, Hadrien; Li, Nan; Rangel, Esteban; Cappello, Franck: Self-adaptive density estimation of particle data (2016)
  17. Sousbie, Thierry; Colombi, Stéphane: ColDICE: A parallel Vlasov-Poisson solver using moving adaptive simplicial tessellation (2016)
  18. Tozoni, Davi C.; Rezende, Pedro J.De; Souza, Cid C.De: Algorithm 966: A practical iterative algorithm for the art gallery problem using integer linear programming (2016)
  19. Agarwal, Pankaj K.; Kaplan, Haim; Rubin, Natan; Sharir, Micha: Kinetic Voronoi diagrams and Delaunay triangulations under polygonal distance functions (2015)
  20. Antonietti, Paola F.; Dedner, Andreas; Madhavan, Pravin; Stangalino, Simone; Stinner, Björn; Verani, Marco: High order discontinuous Galerkin methods for elliptic problems on surfaces (2015)

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