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 335 articles , 4 standard articles )

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  1. Duan, Xianglong; Quan, Chaoyu; Stamm, Benjamin: A boundary-partition-based Voronoi diagram of (d)-dimensional balls: definition, properties, and applications (2020)
  2. Duque, Daniel; Español, Pep: An assignment procedure from particles to mesh that preserves field values (2020)
  3. Ferrada, Héctor; Navarro, Cristóbal A.; Hitschfeld, Nancy: A filtering technique for fast convex hull construction in (\mathbbR^2) (2020)
  4. Guo, Hailong: Surface Crouzeix-Raviart element for the Laplace-Beltrami equation (2020)
  5. Lu, Wuyue; Liu, Ligang: Surface reconstruction via cooperative evolutions (2020)
  6. Maquart, Tristan; Wenfeng, Ye; Elguedj, Thomas; Gravouil, Anthony; Rochette, Michel: 3D volumetric isotopological meshing for finite element and isogeometric based reduced order modeling (2020)
  7. Sanchez-Rivadeneira, A. G.; Shauer, N.; Mazurowski, B.; Duarte, C. A.: A stable generalized/extended (p)-hierarchical FEM for three-dimensional linear elastic fracture mechanics (2020)
  8. Shi, Jia; Beretta, Elena; de Hoop, Maarten V.; Francini, Elisa; Vessella, Sergio: A numerical study of multi-parameter full waveform inversion with iterative regularization using multi-frequency vibroseis data (2020)
  9. Wan, Andy T. S.; Laforest, Marc: A posteriori error estimation for the p-curl problem (2020)
  10. Yang, Baorong; Yao, Junfeng; Wang, Bin; Hu, Jianwei; Pan, Yiling; Pan, Tianxiang; Wang, Wenping; Guo, Xiaohu: P2MAT-NET: learning medial axis transform from sparse point clouds (2020)
  11. Attali, Dominique; Nguyen, Tuong-Bach; Sivignon, Isabelle: ((\delta,\varepsilon))-ball approximation of a shape: definition and complexity (2019)
  12. de Gournay, Frédéric; Kahn, Jonas; Lebrat, Léo: Differentiation and regularity of semi-discrete optimal transport with respect to the parameters of the discrete measure (2019)
  13. Edelsbrunner, Herbert; Ölsböck, Katharina: Holes and dependences in an ordered complex (2019)
  14. González Obando, Daniel Felipe; Olivo-Marin, Jean-Christophe; Wendling, Laurent; Meas-Yedid, Vannary: Vector-based morphological operations on polygons using straight skeletons for digital pathology (2019)
  15. Grande, Jörg: Red-green refinement of simplicial meshes in (d) dimensions (2019)
  16. Guha, Sumanta: Computer graphics through OpenGL. From theory to experiments (2019)
  17. Milenkovic, Victor; Sacks, Elisha; Butt, Nabeel: Fast detection of degenerate predicates in free space construction (2019)
  18. Soto-Francés, Víctor-Manuel; Sarabia-Escrivá, Emilio-José; Pinazo-Ojer, José-Manuel: Consistently oriented dart-based 3D modelling by means of geometric algebra and combinatorial maps (2019)
  19. Valentin Niess, Anne Barnoud, Cristina Cârloganu, Olivier Martineau-Huynh: TURTLE: A C library for an optimistic stepping through a topography (2019) arXiv
  20. Yan, Ke; Cheng, Ho-Lun; Huang, Jing: Representing implicit surfaces satisfying Lipschitz conditions by 4-dimensional point sets (2019)

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