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Kinetic Collision Detection for Convex Fat Objects

  • M. A. Abam
  • M. de Berg
  • S. -H. Poon
  • B. Speckmann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4168)

Abstract

We design compact and responsive kinetic data structures for detecting collisions between n convex fat objects in 3-dimensional space that can have arbitrary sizes. Our main results are:

(i) If the objects are 3-dimensional balls that roll on a plane, then we can detect collisions with a KDS of size O(nlogn) that can handle events in O(logn) time. This structure processes O(n 2) events in the worst case, assuming that the objects follow constant-degree algebraic trajectories.

(ii) If the objects are convex fat 3-dimensional objects of constant complexity that are free-flying in \({\mathbb R}^3\), then we can detect collisions with a KDS of O(nlog6 n) size that can handle events in O(log6 n) time. This structure processes O(n 2) events in the worst case, assuming that the objects follow constant-degree algebraic trajectories. If the objects have similar sizes then the size of the KDS becomes O(n) and events can be handled in O(1) time.

Keywords

Computational Geometry Small Object Collision Detection Tangency Point Simple Polygon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • M. A. Abam
    • 1
  • M. de Berg
    • 1
  • S. -H. Poon
    • 1
  • B. Speckmann
    • 1
  1. 1.Department of Mathematics and Computing ScienceTU EindhovenMB EindhovenThe Netherlands

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