The quickhull algorithm for convex hulls (original) (raw)
Published: 01 December 1996 Publication History
Abstract
The convex hull of a set of points is the smallest convex set that contains the points. This article presents a practical convex hull algorithm that combines the two-dimensional Quickhull algorithm with the general-dimension Beneath-Beyond Algorithm. It is similar to the randomized, incremental algorithms for convex hull and delaunay triangulation. We provide empirical evidence that the algorithm runs faster when the input contains nonextreme points and that it used less memory. computational geometry algorithms have traditionally assumed that input sets are well behaved. When an algorithm is implemented with floating-point arithmetic, this assumption can lead to serous errors. We briefly describe a solution to this problem when computing the convex hull in two, three, or four dimensions. The output is a set of “thick” facets that contain all possible exact convex hulls of the input. A variation is effective in five or more dimensions.
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Published In
ACM Transactions on Mathematical Software Volume 22, Issue 4
Dec. 1996
116 pages
Copyright © 1996 ACM.
Publisher
Association for Computing Machinery
New York, NY, United States
Publication History
Published: 01 December 1996
Published in TOMS Volume 22, Issue 4
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Affiliations
National Institute of Standards and Technology, Guithersburg, MD
C. Bradford Barber
Univ. of Minnesota, Minneapolis
David P. Dobkin
Princeton Univ., Princeton, NJ
Hannu Huhdanpaa
Configured Energy Systems, Inc., Plymouth, MN