Separation­sensitive collision detection for convex objects

Written with Leonidas J. Guibas, Jorge Stolfi, and Li Zhang.
Proceedings of the 10th Annual ACM­SIAM Symposium on Discrete Algorithms, 327-336, 1999.
We develop a class of new kinetic data structures for collision detection between moving convex polytopes; these structures are sensitive to the separation of the polytopes during their motion. For two polygons in the plane, let D be the maximum diameter of the polygons, and let s be the minimum distance between them during their motion. Our separation certificate changes O(log(D/s)) times when the relative motion of the two polygons is a translation along a straight line or convex curve, O(sqrt{D/s}) for translation along an algebraic trajectory, and O(D/s) for algebraic rigid motion (translation and rotation). Each certificate update is performed in O(log(D/s)) time. Variants of these data structures are also shown that exhibit hysteresis--after a separation certificate fails, the new certificate cannot fail again until the objects have moved by some constant fraction of their current separation. We can then bound the number of events by the combinatorial size of a certain cover of the motion path by balls.


Publications - Jeff Erickson ( 14 Feb 2002