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The quickhull algorithm for convex hulls

Editor: Ronald Boisvert Authors:

C. Bradford Barber,

David P. Dobkin,

Hannu HuhdanpaaAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 22, Issue 4

Pages 469 - 483

https://doi.org/10.1145/235815.235821

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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Index Terms

The quickhull algorithm for convex hulls
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 22, Issue 4

Dec. 1996

116 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/235815

Editor:
Ronald Boisvert
National Institute of Standards and Technology, Guithersburg, MD

Issue’s Table of Contents

Copyright © 1996 ACM.

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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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