Kinetic collision detection for convex fat objects

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(nlog∈n) that can handle events in O(log∈ ² n) 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 ℝ ³, then we can detect collisions with a KDS of O(nlog∈ ⁶ n) 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(log∈n) time.