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. Herbert-Voss, Ariel; Hirn, Matthew J.; McCollum, Frederick: Computing minimal interpolants in $C^1,1(\mathbbR^d)$ (2017)
  2. Li, Jingzhi; Liu, Hongyu; Wang, Yuliang: Recovering an electromagnetic obstacle by a few phaseless backscattering measurements (2017)
  3. Rangarajan, Ramsharan: On the resolution of certain discrete univariate max-min problems (2017)
  4. Rudloff, Birgit; Ulus, Firdevs; Vanderbei, Robert: A parametric simplex algorithm for linear vector optimization problems (2017)
  5. Toth, Csaba D. (ed.); Goodman, Jacob E. (ed.); O’Rourke, Joseph (ed.): Handbook of discrete and computational geometry (2017)
  6. Widom, M.: Frequency estimate for multicomponent crystalline compounds (2017)
  7. Ziegelmeier, Lori; Kirby, Michael; Peterson, Chris: Stratifying high-dimensional data based on proximity to the convex hull boundary (2017)
  8. Alves, Maria João; Costa, João Paulo: Graphical exploration of the weight space in three-objective mixed integer linear programs (2016)
  9. Beyhaghi, Pooriya; Cavaglieri, Daniele; Bewley, Thomas: Delaunay-based derivative-free optimization via global surrogates. I: Linear constraints (2016)
  10. Bodart, Olivier; Cayol, Valérie; Court, Sébastien; Koko, Jonas: XFEM-based fictitious domain method for linear elasticity model with crack (2016)
  11. Edeling, W.N.; Dwight, R.P.; Cinnella, P.: Simplex-stochastic collocation method with improved scalability (2016)
  12. Groot, Noortje; De Schutter, Bart; Hellendoorn, Hans: Optimal affine leader functions in reverse Stackelberg games. Existence conditions and characterization (2016)
  13. Lin, Zhiyuan; Kwan, Raymond S.K.: Local convex hulls for a special class of integer multicommodity flow problems (2016)
  14. Peterka, Tom; Croubois, Hadrien; Li, Nan; Rangel, Esteban; Cappello, Franck: Self-adaptive density estimation of particle data (2016)
  15. Yoo, Yongseok; Koyluoglu, O. Ozan; Vishwanath, Sriram; Fiete, Ila: Multi-periodic neural coding for adaptive information transfer (2016)
  16. Zhang, Qi; Grossmann, Ignacio E.; Sundaramoorthy, Arul; Pinto, Jose M.: Data-driven construction of convex region surrogate models (2016)
  17. Bazovkin, Pavel; Mosler, Karl: A general solution for robust linear programs with distortion risk constraints (2015)
  18. Calef, Matthew; Griffiths, Whitney; Schulz, Alexia: Estimating the number of stable configurations for the generalized Thomson problem (2015)
  19. 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)
  20. Jenkins, Thomas G.; Held, Eric D.: Coupling extended magnetohydrodynamic fluid codes with radiofrequency ray tracing codes for fusion modeling (2015)

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