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(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.
Original language | English |
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Pages (from-to) | 457-473 |
Number of pages | 17 |
Journal | Algorithmica |
Volume | 53 |
Issue number | 4 |
DOIs | |
Publication status | Published - Apr 2009 |
Externally published | Yes |
Keywords
- Collision detection
- Fat objects
- Kinetic data structures
ASJC Scopus subject areas
- General Computer Science
- Computer Science Applications
- Applied Mathematics