Kinetic collision detection for convex fat objects

Authors:
M. A. Abam;M. de Berg;S.-H. Poon;B. Speckmann
Affiliations:
Department of Mathematics and Computing Science, TU Eindhoven, MB Eindhoven, The Netherlands;Department of Mathematics and Computing Science, TU Eindhoven, MB Eindhoven, The Netherlands;Department of Mathematics and Computing Science, TU Eindhoven, MB Eindhoven, The Netherlands;Department of Mathematics and Computing Science, TU Eindhoven, MB Eindhoven, The Netherlands
Venue:
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
Year:
2006

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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(n2) 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 R3, then we can detect collisions with a KDS of O(nlog6n) size that can handle events in O(log6n) time. This structure processes O(n2) 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.