English

The convex hull of a random set of points, plotted in 3D

Noun

convex hull ‎(plural convex hulls)

1. (mathematics) The smallest convex set of points in which a given set of points is contained.
   • 1994, David Eppstein, Chapter 10: Average Case Analysis of Dynamic Geometric Optimization, Association of Computing Machinery, Society for Industrial and Applied Mathematics, Proceedings of the Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, page 83,

     This problem can be solved in time O(n^c) by combining a weight-balanced tree of the convex hull vertices with a farthest neighbor data structure of Agarwal and Matoušek [2].

   • 2005, A.D. Alexandrov, Convex Polyhedra, page 23,

     Thus, the polyhedron and the convex hull of the set of its vertices coincide, which was to be proved.

     Since the convex hull of a set M is determined uniquely from M, Theorem 1 implies that a bounded solid polyhedron and its surface, i.e., a closed convex polyhedron, are determined uniquely from its vertices.

   • 2007, Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, page 185,

     The convex hull of a compact subset of an infinite dimensional topological vector space need not be a compact set.

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