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COMPGEOM
1991
ACM

A Pivoting Algorithm for Convex Hulls and Vertex Enumeration of Arrangements and Polyhedra

10 years 4 months ago
A Pivoting Algorithm for Convex Hulls and Vertex Enumeration of Arrangements and Polyhedra
We present a new pivot-based algorithm which can be used with minor modification for the enumeration of the facets of the convex hull of a set of points, or for the enumeration of the vertices of an arrangement or of a convex polyhedron, in arbitrary dimension. The algorithm has the following properties: (a) No additional storage is required beyond the input data; (b) The output list produced is free of duplicates; (c) The algorithm is extremely simple, requires no data structures, and handles all degenerate cases; (d) The running time is output sensitive for non-degenerate inputs; (e) The algorithm is easy to efficiently parallelize. For example, the algorithm finds the v vertices of a polyhedron in Rd defined by a nondegenerate system of n inequalities (or dually, the v facets of the convex hull of n points in Rd , where each facet contains exactly d given points) in time O(ndv) and O(nd) space. The v vertices in a simple arrangement of n hyperplanes in Rd can be found in O(n2 d...
David Avis, Komei Fukuda
Added 27 Aug 2010
Updated 27 Aug 2010
Type Conference
Year 1991
Where COMPGEOM
Authors David Avis, Komei Fukuda
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