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Special Topics:Computational Geometry

Qhull with random perturbations by Brad Barber


This sphere is an approximate convex hull of 200 cospherical points. During its construction, every computation was randomly perturbed by a number between -0.01 and 0.01. Despite the perturbations, all pairs of neighboring facets are convex. This demonstrates that the program, Qhull, can handle arbitrary amounts of round-off error.

Each approximate facet consists of an inner plane and an outer plane. The outer planes are above all of the points (red-yellow lines) while the inner planes are below the vertices (white spheres). The exact convex hull lies between the inner and outer planes.

How to make it: rbox 200 s B1 | qhull C-0 Qc R0.01 Gpav >a

Image created: April 1995

[Qhull with random perturbations]

Copyright © April 1995 by The Geometry Center, Univerity of Minnesota. All rights reserved.
For permission to use this image, contact permission@geom.math.uiuc.edu.

External viewing: small (100x100 3k gif), medium (500x396 27k gif), or original size (1278x1012 219k tiff).

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Created: Sat May 22 23:17:50 CDT 1999 --- Last modified: Sat May 22 23:17:50 CDT 1999