DMCA
The Quickhull algorithm for convex hulls (1996)
Cached
Download Links
- [www.cise.ufl.edu]
- [geom.umn.edu]
- [ftp.cs.princeton.edu]
- DBLP
Other Repositories/Bibliography
| Venue: | ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE |
| Citations: | 699 - 0 self |
BibTeX
@ARTICLE{Barber96thequickhull,
author = {C. Bradford Barber and David P. Dobkin and Hannu Huhdanpaa},
title = {The Quickhull algorithm for convex hulls},
journal = {ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE},
year = {1996},
volume = {22},
number = {4},
pages = {469--483}
}
Share
 |
 |
 |
 |
||
OpenURL
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 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.
Keyphrases
convex hull quickhull algorithm computational geometry algorithm incremental algorithm nonextreme point general-dimension beneath-beyond algorithm thick facet convex set empirical evidence delaunay triangulation serious error possible exact convex hull practical convex hull algorithm two-dimensional quickhull algorithm input set
