Reliable Collision Detection for Time-Dependent Parametric Surfaces

Reliable Collision Detection for Time-Dependent Parametric Surfaces We improve on an algorithm by Von Herzen, Barr, and Zatz (HBZ) to detect geometric collisions between pairs of time-dependent parametric surfaces. The HBZ algorithm uses upper bounds on the parametric derivatives to guarantee detection of collisions and near misses, thus avoiding the defects of algorithms which sample the surfaces, possibly missing sharp spikes. Unfortunately, the user of the HBZ algorithm must supply not only routines computing the surface functions, but also routines bounding every component in the Jacobian of these surface functions over an arbitrary parametric range. Although they give helpful analyses for several types of surfaces, HBZ admit the need to provide Jacobian bounding routines as a disadvantage. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Reliable Collision Detection for Time-Dependent Parametric Surfaces

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 1998 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1024411614890
Publisher site
See Article on Publisher Site

Abstract

We improve on an algorithm by Von Herzen, Barr, and Zatz (HBZ) to detect geometric collisions between pairs of time-dependent parametric surfaces. The HBZ algorithm uses upper bounds on the parametric derivatives to guarantee detection of collisions and near misses, thus avoiding the defects of algorithms which sample the surfaces, possibly missing sharp spikes. Unfortunately, the user of the HBZ algorithm must supply not only routines computing the surface functions, but also routines bounding every component in the Jacobian of these surface functions over an arbitrary parametric range. Although they give helpful analyses for several types of surfaces, HBZ admit the need to provide Jacobian bounding routines as a disadvantage.

Journal

Reliable ComputingSpringer Journals

Published: Oct 14, 2004

References

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