
 Qhull 2002.1 2002/8/20

        http://www.geom.umn.edu/software/qhull
	http://www.geom.umn.edu/software/download/qhull.html
        http://savannah.gnu.org/projects/qhull/
        http://www6.uniovi.es/ftp/pub/mirrors/geom.umn.edu/software/ghindex.html
        http://www.geomview.org

Qhull computes convex hulls, Delaunay triangulations, Voronoi diagrams, 
furthest-site Voronoi diagrams, and halfspace intersections about a point. 
It runs in 2-d, 3-d, 4-d, or higher.  It implements the Quickhull algorithm 
for computing convex hulls.   Qhull handles round-off errors from floating 
point arithmetic.  It can approximate a convex hull.

The program includes options for hull volume, facet area, partial hulls,
input transformations, randomization, tracing, multiple output formats, and
execution statistics.  The program can be called from within your application.
You can view the results in 2-d, 3-d and 4-d with Geomview.

To download Qhull:

        http://www.geom.umn.edu/software/download/qhull.html

Download qhull-96.ps for:

        Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, 
        "The Quickhull Algorithm for Convex Hulls," ACM
        Trans. on Mathematical Software, Dec. 1996.
        http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/
	http://www.geom.umn.edu/software/qhull/qhull-96.ps

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 non-extreme
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.  

