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.
M.A. and S.-H.P. were supported by the Netherlands’ Organisation for Scientific Research (NWO) under project no. 612.065.307. M.d.B. was supported by the Netherlands’ Organisation for Scientific Research (NWO) under project no. 639.023.301.
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Abam, M.A., de Berg, M., Poon, S.H., Speckmann, B. (2006). Kinetic Collision Detection for Convex Fat Objects. In: Azar, Y., Erlebach, T. (eds) Algorithms – ESA 2006. ESA 2006. Lecture Notes in Computer Science, vol 4168. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11841036_4
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DOI: https://doi.org/10.1007/11841036_4
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