Qhull

The convex hull of a point set P is the smallest convex set that contains P. If P is finite, the convex hull defines a matrix A and a vector b such that for all x in P, Ax+b <= [0,...].Qhull computes the convex hull in 2-d, 3-d, 4-d, and higher dimensions. Qhull represents a convex hull as a list of facets. Each facet has a set of vertices, a set of neighboring facets, and a halfspace. A halfspace is defined by a unit normal and an offset (i.e., a row of A and an element of b).Qhull accounts for round-off error. It returns ”thick” facets defined by two parallel hyperplanes. The outer planes contain all input points. The inner planes exclude all output vertices. See Imprecise convex hulls.Qhull may be used for the Delaunay triangulation or the Voronoi diagram of a set of points. It may be used for the intersection of halfspaces.


References in zbMATH (referenced in 297 articles )

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  1. Bruno, A. D.: Normal form of a Hamiltonian system with a periodic perturbation (2020)
  2. Chester, Shai M.; Landry, Walter; Liu, Junyu; Poland, David; Simmons-Duffin, David; Su, Ning; Vichi, Alessandro: Carving out OPE space and precise O(2) model critical exponents (2020)
  3. Crombez, Loïc; da Fonseca, Guilherme D.; Gerard, Yan: Efficiently testing digital convexity and recognizing digital convex polygons (2020)
  4. Fagbemi, Samuel; Tahmasebi, Pejman: Coupling pore network and finite element methods for rapid modelling of deformation (2020)
  5. Ferrada, Héctor; Navarro, Cristóbal A.; Hitschfeld, Nancy: A filtering technique for fast convex hull construction in (\mathbbR^2) (2020)
  6. Hahn, Artur; Bode, Julia; Krüwel, Thomas; Kampf, Thomas; Buschle, Lukas R.; Sturm, Volker J. F.; Zhang, Ke; Tews, Björn; Schlemmer, Heinz-Peter; Heiland, Sabine; Bendszus, Martin; Ziener, Christian H.; Breckwoldt, Michael O.; Kurz, Felix T.: Gibbs point field model quantifies disorder in microvasculature of U87-glioblastoma (2020)
  7. Menzel, Peter; Teichmann, Jakob; van den Boogaart, Karl Gerald: Efficient representation of Laguerre mosaics with an application to microstructure simulation of complex ore (2020)
  8. Oujia, Thibault; Matsuda, Keigo; Schneider, Kai: Divergence and convergence of inertial particles in high-Reynolds-number turbulence (2020)
  9. Ping, Xubin; Yang, Sen; Ding, Baocang; Raïssi, Tarek; Li, Zhiwu: Observer-based output feedback robust MPC via zonotopic set-membership state estimation for LPV systems with bounded disturbances and noises (2020)
  10. Polyrakis, Ioannis A.: The NMF problem and lattice-subspaces (2020)
  11. Ranocha, Hendrik; Ketcheson, David I.: Relaxation Runge-Kutta methods for Hamiltonian problems (2020)
  12. Shyamalkumar, Nariankadu D.; Tao, Siyang: On tail dependence matrices. The realization problem for parametric families (2020)
  13. Tewari, Sourav Mukul; Ayyagari, Ravi Sastri: A novel approach to generating microstructurally-aware non-convex domains (2020)
  14. Abdol Azis, Mohd Hazmil; Evrard, Fabien; van Wachem, Berend: An immersed boundary method for flows with dense particle suspensions (2019)
  15. Bryuno, A. D.: On the parametrization of an algebraic curve (2019)
  16. Chen, Yewang; Zhou, Lida; Tang, Yi; Singh, Jai Puneet; Bouguila, Nizar; Wang, Cheng; Wang, Huazhen; Du, Jixiang: Fast neighbor search by using revised (k)-d tree (2019)
  17. Court, Sébastien: A fictitious domain approach for a mixed finite element method solving the two-phase Stokes problem with surface tension forces (2019)
  18. Crombez, Loïc; da Fonseca, Guilherme D.; Gérard, Yan: Efficient algorithms to test digital convexity (2019)
  19. Efremov, R. V.: Complexity of methods for approximating convex compact bodies by double description polytopes and complexity bounds for a hyperball (2019)
  20. Halder, Yous V.; Sanderse, Benjamin; Koren, Barry: An adaptive minimum spanning tree multielement method for uncertainty quantification of smooth and discontinuous responses (2019)

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