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.

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  1. Ferrada, Héctor; Navarro, Cristóbal A.; Hitschfeld, Nancy: A filtering technique for fast convex hull construction in (\mathbbR^2) (2020)
  2. 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)
  3. Abdol Azis, Mohd Hazmil; Evrard, Fabien; van Wachem, Berend: An immersed boundary method for flows with dense particle suspensions (2019)
  4. Bryuno, A. D.: On the parametrization of an algebraic curve (2019)
  5. Court, Sébastien: A fictitious domain approach for a mixed finite element method solving the two-phase Stokes problem with surface tension forces (2019)
  6. Crombez, Loïc; da Fonseca, Guilherme D.; Gérard, Yan: Efficient algorithms to test digital convexity (2019)
  7. Efremov, R. V.: Complexity of methods for approximating convex compact bodies by double description polytopes and complexity bounds for a hyperball (2019)
  8. Halder, Yous V.; Sanderse, Benjamin; Koren, Barry: An adaptive minimum spanning tree multielement method for uncertainty quantification of smooth and discontinuous responses (2019)
  9. Kilingar, N. G.; Ehab Moustafa Kamel, K.; Sonon, B.; Massart, T. J.; Noels, L.: Computational generation of open-foam representative volume elements with morphological control using distance fields (2019)
  10. Nguyen Kieu Linh; Song, Chanyoung; Ryu, Joonghyun; Phan Thanh An; Hoang, Nam-Dũng; Kim, Deok-Soo: QuickhullDisk: a faster convex hull algorithm for disks (2019)
  11. Qu, Rui; Liu, Shu-Shen; Wang, Ze-Jun; Chen, Fu: A novel method based on similarity and triangulation for predicting the toxicities of various binary mixtures (2019)
  12. Rathke, Fabian; Schnörr, Christoph: Fast multivariate log-concave density estimation (2019)
  13. Reinstädler, S.; Kowalsky, U.; Dinkler, D.: Analysis of landslides employing a space-time single-phase level-set method (2019)
  14. Sánchez, Marcelino; Bernal, Miguel: LMI-based robust control of uncertain nonlinear systems via polytopes of polynomials (2019)
  15. Škulj, Damjan: Errors bounds for finite approximations of coherent lower previsions on finite probability spaces (2019)
  16. Zolotykh, Nikolai Yu.; Bastrakov, Sergei I.: Two variations of graph test in double description method (2019)
  17. Badia, Santiago; Martin, Alberto F.; Verdugo, Francesc: Mixed aggregated finite element methods for the unfitted discretization of the Stokes problem (2018)
  18. Brunel, Victor-Emmanuel: Methods for estimation of convex sets (2018)
  19. Endres, Stefan C.; Sandrock, Carl; Focke, Walter W.: A simplicial homology algorithm for Lipschitz optimisation (2018)
  20. Gamby, Ask Neve; Katajainen, Jyrki: Convex-hull algorithms: implementation, testing, and experimentation (2018)

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