convex hull
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English
[edit]Noun
[edit]convex hull (plural convex hulls)
- (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(nc) 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[1], 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.
- 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,
Synonyms
[edit]- (smallest convex set of points containing a given set): convex envelope, linear span, span
Translations
[edit]convex set of points
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Further reading
[edit]- Convex geometry on Wikipedia.Wikipedia
- Convex set on Wikipedia.Wikipedia