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. Bodart, Olivier; Cayol, Valérie; Court, Sébastien; Koko, Jonas: XFEM-based fictitious domain method for linear elasticity model with crack (2016)
  2. Edeling, W.N.; Dwight, R.P.; Cinnella, P.: Simplex-stochastic collocation method with improved scalability (2016)
  3. Groot, Noortje; De Schutter, Bart; Hellendoorn, Hans: Optimal affine leader functions in reverse Stackelberg games. Existence conditions and characterization (2016)
  4. Lin, Zhiyuan; Kwan, Raymond S.K.: Local convex hulls for a special class of integer multicommodity flow problems (2016)
  5. Peterka, Tom; Croubois, Hadrien; Li, Nan; Rangel, Esteban; Cappello, Franck: Self-adaptive density estimation of particle data (2016)
  6. Yoo, Yongseok; Koyluoglu, O. Ozan; Vishwanath, Sriram; Fiete, Ila: Multi-periodic neural coding for adaptive information transfer (2016)
  7. Bazovkin, Pavel; Mosler, Karl: A general solution for robust linear programs with distortion risk constraints (2015)
  8. Calef, Matthew; Griffiths, Whitney; Schulz, Alexia: Estimating the number of stable configurations for the generalized Thomson problem (2015)
  9. Contento, Lorenzo; Ern, Alexandre; Vermiglio, Rossana: A linear-time approximate convex envelope algorithm using the double Legendre-Fenchel transform with application to phase separation (2015)
  10. Linh, Nguyen Kieu; Muu, Le Dung: A convex hull algorithm for solving a location problem (2015)
  11. Liu, Xiaohui; Ren, Haiping; Wang, Guofu: Computing halfspace depth contours based on the idea of a circular sequence (2015)
  12. Piffl, Martin; Stadlober, Ernst: The depth-design: an efficient generation of high dimensional computer experiments (2015)
  13. Ping, Xubin; Sun, Ning: Dynamic output feedback robust model predictive control via zonotopic set-membership estimation for constrained quasi-LPV systems (2015)
  14. Ballerstein, Martin; Michaels, Dennis: Extended formulations for convex envelopes (2014)
  15. Dhara, Anulekha; Luc, Dinh The: A solution method for linear variational relation problems (2014)
  16. Hamel, Andreas H.; Löhne, Andreas; Rudloff, Birgit: Benson type algorithms for linear vector optimization and applications (2014)
  17. Liu, Xiaohui; Zuo, Yijun: Computing projection depth and its associated estimators (2014)
  18. Machucho-Cadena, Rubén; Rivera-Rovelo, Jorge; Bayro-Corrochano, Eduardo: Geometric techniques for 3D tracking of ultrasound sensor, tumor segmentation in ultrasound images, and 3D reconstruction (2014)
  19. Olesen, Ole B.: A homothetic reference technology in data envelopment analysis (2014)
  20. Pendharkar, Parag C.; Troutt, Marvin D.: Interactive classification using data envelopment analysis (2014)

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