The Quickhull Algorithm for Convex Hulls
Report ID: TR-565-95Author: Huhdanpaa, Hannu / Barber, C. Bradford / Dobkin, David P.
Date: 1995-01-00
Pages: 15
Download Formats: |Postscript|
Abstract:
The convex hull of a set of points is the smallest convex set that contains the points. This paper 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 uses 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 serious 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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This technical report has been published as
- The Quickhull Algorithm for Convex Hulls.
C. Bradford Barber, David P. Dobkin, and Hannu Huhdanpaa, ACM
Trans. on Math. Software, vol. 22, no. 4,
469-483, December 1996.
- Here is the software described in this paper and the tables for the paper can be found in BarberDobkinHuhdanpaa.tables.ps.Z, 11K.