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 320 articles )

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  1. Apte, Sourabh V.; Oujia, Thibault; Matsuda, Keigo; Kadoch, Benjamin; He, Xiaoliang; Schneider, Kai: Clustering of inertial particles in turbulent flow through a porous unit cell (2022)
  2. Wang, Jue: Optimal sequential multiclass diagnosis (2022)
  3. Zhu, Qingyuan; Aparicio, Juan; Li, Feng; Wu, Jie; Kou, Gang: Determining closest targets on the extended facet production possibility set in data envelopment analysis: modeling and computational aspects (2022)
  4. Badia, Santiago; Caicedo, Manuel A.; Martín, Alberto F.; Principe, Javier: A robust and scalable unfitted adaptive finite element framework for nonlinear solid mechanics (2021)
  5. Baňas, Ľubomír; Ferrari, Giorgio; Randrianasolo, Tsiry A.: Numerical approximation of the value of a stochastic differential game with asymmetric information (2021)
  6. Bruno, A. D.; Batkhin, A. B.: Algorithms and programs for calculating the roots of polynomial of one or two variables (2021)
  7. Dellnitz, Andreas; Reucher, Elmar; Kleine, Andreas: Efficiency evaluation in data envelopment analysis using strong defining hyperplanes. A cross-efficiency framework (2021)
  8. Hokanson, Jeffrey M.; Constantine, Paul G.: A Lipschitz matrix for parameter reduction in computational science (2021)
  9. Huang, Eric; Cheng, Xianyi; Mason, Matthew T.: Efficient contact mode enumeration in 3D (2021)
  10. Li, Lingfeng; Luo, Shousheng; Tai, Xue-Cheng; Yang, Jiang: A new variational approach based on level-set function for convex hull problem with outliers (2021)
  11. Magron, Victor; Safey El Din, Mohab: On exact Reznick, Hilbert-Artin and Putinar’s representations (2021)
  12. Yuan, Tianran; Zhang, Hongsheng; Liu, Hao; Du, Juan; Yu, Huiming; Wang, Yimin; Xu, Yabin: Watertight 2-manifold 3D bone surface model reconstruction from CT images based on visual hyper-spherical mapping (2021)
  13. Yu, Yue; Grazioli, Gianmarc; Phillips, Nolan E.; Butts, Carter T.: Local graph stability in exponential family random graph models (2021)
  14. Zhang, Kewei; Orlando, Antonio; Crooks, Elaine: Compensated convexity on bounded domains, mixed Moreau envelopes and computational methods (2021)
  15. An, Phan Thanh; Hoang, Nam Dũng; Linh, Nguyen Kieu: An efficient improvement of gift wrapping algorithm for computing the convex hull of a finite set of points in (\mathbbR^n) (2020)
  16. Awasthi, Pranjal; Kalantari, Bahman; Zhang, Yikai: Robust vertex enumeration for convex hulls in high dimensions (2020)
  17. Bruno, A. D.: Normal form of a Hamiltonian system with a periodic perturbation (2020)
  18. Chen, Zhao-Yue; Imholz, Maurice; Li, Liu; Faes, Matthias; Moens, David: Transient landing dynamics analysis for a lunar lander with random and interval fields (2020)
  19. 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)
  20. Crombez, Loïc; da Fonseca, Guilherme D.; Gerard, Yan: Efficiently testing digital convexity and recognizing digital convex polygons (2020)

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