Kinetic Collision Detection for Convex Fat Objects

摘要

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. Otir main results are:rn(i) If the objects are 3-dimensional balls that roll on a plane, then we can detect collisions with a KDS of size O(n log n) that can handle events in O(log!2n) lime. This structure processes O(n~2) events in the worst case, assuming that the objects follow constant-degree algebraic trajectories.rn(ii) If the objects arc convex fat 3-dimensional objects of constant complexity that are free-flying in R~3, then we can detect collisions with a KDS of O(n log~6n) size that can handle events in O(log~7 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(logn) time.