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. Kuti, József; Galambos, Péter: Affine tensor product model transformation (2018)
  2. Lin, Chia-Hsiang; Wu, Ruiyuan; Ma, Wing-Kin; Chi, Chong-Yung; Wang, Yue: Maximum volume inscribed ellipsoid: a new simplex-structured matrix factorization framework via facet enumeration and convex optimization (2018)
  3. Rahman, Adam; Oldford, R. Wayne: Euclidean distance matrix completion and point configurations from the minimal spanning tree (2018)
  4. Zolotykh, Nikolaĭ Yur’evich; Kubarev, Valentin Konstantinovich; Lyalin, Sergeĭ Sergeevich: Double description method over the field of algebraic numbers (2018)
  5. Ahmadabadi, Alireza; Ucer, Burcu Hudaverdi: Bivariate nonparametric estimation of the Pickands dependence function using Bernstein copula with kernel regression approach (2017)
  6. Debnath, Dipsikha; Gainer, James S.; Kilic, Can; Kim, Doojin; Matchev, Konstantin T.; Yang, Yuan-Pao: Detecting kinematic boundary surfaces in phase space: particle mass measurements in SUSY-like events (2017)
  7. Goebel, Gregor; Allgöwer, Frank: Semi-explicit MPC based on subspace clustering (2017)
  8. Herbert-Voss, Ariel; Hirn, Matthew J.; McCollum, Frederick: Computing minimal interpolants in $C^1,1(\mathbbR^d)$ (2017)
  9. Kabaria, Hardik; Lew, Adrian J.: Universal meshes for smooth surfaces with no boundary in three dimensions (2017)
  10. Kaddani, Sami; Vanderpooten, Daniel; Vanpeperstraete, Jean-Michel; Aissi, Hassene: Weighted sum model with partial preference information: application to multi-objective optimization (2017)
  11. Kuti, József; Galambos, Péter; Baranyi, Péter: Minimal volume simplex (MVS) polytopic model generation and manipulation methodology for TP model transformation (2017)
  12. Li, Jingzhi; Liu, Hongyu; Wang, Yuliang: Recovering an electromagnetic obstacle by a few phaseless backscattering measurements (2017)
  13. Rangarajan, Ramsharan: On the resolution of certain discrete univariate max-min problems (2017)
  14. Rudloff, Birgit; Ulus, Firdevs; Vanderbei, Robert: A parametric simplex algorithm for linear vector optimization problems (2017)
  15. Sarkar, Apurba; Biswas, Arindam; Dutt, Mousumi; Bhowmick, Partha; Bhattacharya, Bhargab B.: A linear-time algorithm to compute the triangular hull of a digital object (2017)
  16. Toth, Csaba D. (ed.); Goodman, Jacob E. (ed.); O’Rourke, Joseph (ed.): Handbook of discrete and computational geometry (2017)
  17. Waki, Hayato; Nae, Florin: Boundary modeling in model-based calibration for automotive engines via the vertex representation of the convex hulls (2017)
  18. Weir, William H.; Emmons, Scott; Gibson, Ryan; Taylor, Dane; Mucha, Peter J.: Post-processing partitions to identify domains of modularity optimization (2017)
  19. Widom, M.: Frequency estimate for multicomponent crystalline compounds (2017)
  20. Yang, Zili: Likelihood of environmental coalitions and the number of coalition members: evidences from an IAM model (2017)

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