Publication

Extended convex hull

Thomas Liebling, Komei Fukuda
2001
Journal Articles

Abstract

In this paper we address the problem of computing a minimal representation of the convex hull of the union of k H- polytopes in . Our method applies the reverse search algorithm to a shelling ordering of the facets of the convex hull. Efficient wrapping is done by projecting the polytopes onto the two-dimensional space and solving a linear program. The resulting algorithm is polynomial in the sizes of input and output under the general position assumption.

Official source

https://infoscience.epfl.ch/entities/publication/ff6fda6a-b78d-41b2-96af-f77dc7c69c64

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Thomas Liebling, Komei Fukuda
2001
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/ff6fda6a-b78d-41b2-96af-f77dc7c69c64

About this result

Related concepts (32)

Polytope

In elementary geometry, a polytope is a geometric object with flat sides (faces). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions n as an n-dimensional polytope or n-polytope. For example, a two-dimensional polygon is a 2-polytope and a three-dimensional polyhedron is a 3-polytope. In this context, "flat sides" means that the sides of a (k + 1)-polytope consist of k-polytopes that may have (k – 1)-polytopes in common.

Regular polytope

In mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. All its elements or j-faces (for all 0 ≤ j ≤ n, where n is the dimension of the polytope) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are regular polytopes of dimension ≤ n. Regular polytopes are the generalized analog in any number of dimensions of regular polygons (for example, the square or the regular pentagon) and regular polyhedra (for example, the cube).

Abstract polytope

In mathematics, an abstract polytope is an algebraic partially ordered set which captures the dyadic property of a traditional polytope without specifying purely geometric properties such as points and lines. A geometric polytope is said to be a realization of an abstract polytope in some real N-dimensional space, typically Euclidean. This abstract definition allows more general combinatorial structures than traditional definitions of a polytope, thus allowing new objects that have no counterpart in traditional theory.

Related publications (1)

Extended convex hull

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