Dictionary

convex hull en · NOUN

Meanings

1. The smallest convex set of points in which a given set of points is contained.
   • The convex hull of a compact subset of an infinite dimensional topological vector space need not be a compact set. 2007, Charalambos D. Aliprantis, Kim C. Border, Infinite Dimensional Analysis: A Hitchhiker's Guide, page 185:
   • 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(nᶜ) by combining a weight-balanced tree of the convex hull vertices with a farthest neighbor data structure of Agarwal and Matoušek [2].
   • 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. 2005, A.D. Alexandrov, Convex Polyhedra, page 23:

Forms

Synonyms

convex envelope (smallest convex set of points containing a given set) · span (smallest convex set of points containing a given set) · linear span (smallest convex set of points containing a given set)

Translations (5)

fi konveksi verho (convex set of points) · it inviluppo convesso (convex set of points) · fr enveloppe convexe (convex set of points) · it involucro convesso (convex set of points) · cs konvexní obal (convex set of points)