CGAL

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 305 articles , 4 standard articles )

Showing results 1 to 20 of 305.
Sorted by year (citations)

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  1. Attali, Dominique; Nguyen, Tuong-Bach; Sivignon, Isabelle: ((\delta,\varepsilon))-ball approximation of a shape: definition and complexity (2019)
  2. 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)
  3. Grande, Jörg: Red-green refinement of simplicial meshes in (d) dimensions (2019)
  4. Guha, Sumanta: Computer graphics through OpenGL. From theory to experiments (2019)
  5. 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)
  6. Baram, Alon; Fogel, Efi; Halperin, Dan; Hemmer, Michael; Morr, Sebastian: Exact Minkowski sums of polygons with holes (2018)
  7. Beaude, Laurence; Beltzung, Thibaud; Brenner, Konstantin; Lopez, Simon; Masson, Roland; Smai, Farid; Thebault, Jean-Frédéric; Xing, Feng: Parallel geothermal numerical model with fractures and multi-branch wells (2018)
  8. Bus, Norbert; Mustafa, Nabil H.; Ray, Saurabh: Practical and efficient algorithms for the geometric hitting set problem (2018)
  9. Cabello, Sergio; Milinković, Lazar: Two optimization problems for unit disks (2018)
  10. Calvin, James; Gimbutienė, Gražina; Phillips, William O.; Žilinskas, Antanas: On convergence rate of a rectangular partition based global optimization algorithm (2018)
  11. D’Amore, Fabrizio; Franciosa, Paolo G.: A low arithmetic-degree algorithm for computing proximity graphs (2018)
  12. Haque, Tasnuva; Lucet, Yves: A linear-time algorithm to compute the conjugate of convex piecewise linear-quadratic bivariate functions (2018)
  13. Kallus, Yoav; Romik, Dan: Improved upper bounds in the moving sofa problem (2018)
  14. Khan, Dawar; Yan, Dong-Ming; Wang, Yiqun; Hu, Kaimo; Ye, Juntao; Zhang, Xiaopeng: High-quality 2D mesh generation without obtuse and small angles (2018)
  15. Kusano, Genki; Fukumizu, Kenji; Hiraoka, Yasuaki: Kernel method for persistence diagrams via kernel embedding and weight factor (2018)
  16. Mamageishvili, Akaki; Mihalák, Matúš; Montemezzani, Simone: Improved bounds on equilibria solutions in the network design game (2018)
  17. Mérigot, Quentin; Meyron, Jocelyn; Thibert, Boris: An algorithm for optimal transport between a simplex soup and a point cloud (2018)
  18. Obayashi, Ippei; Hiraoka, Yasuaki; Kimura, Masao: Persistence diagrams with linear machine learning models (2018)
  19. Peter G. Lelièvre; Angela E. Carter-McAuslan; Michael W. Dunham; Drew J. Jones; Mariella Nalepa; Chelsea L.Squires; Cassandra J. Tycholiz; Marc A. Vallée; Colin G .Farquharson: FacetModeller: Software for manual creation, manipulation and analysis of 3D surface-based models (2018) not zbMATH
  20. Sheng, Bin; Liu, Bowen; Li, Ping; Fu, Hongbo; Ma, Lizhuang; Wu, Enhua: Accelerated robust Boolean operations based on hybrid representations (2018)

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Further publications can be found at: http://www.cgal.org/Manual/3.2/doc_html/cgal_manual/biblio.html