Deformable Free-Space Tilings for Kinetic Collision Detection

We present kinetic data structures for detecting collisions between a set of polygons that are moving continuously. Unlike classical collision detection methods that rely on bounding volume hierarchies, our method is based on deformable tilings of the free space surrounding the polygons. The basic shape of our tiles is that of a pseudo-triangle, a shape sufficiently flexible to allow extensive deformation, yet structured enough to make detection of self-collisions easy. We show different schemes for maintaining pseudotriangulations as a kinetic data structure, and we analyze their performance. Specifically, we first describe an algorithm for maintaining a pseudo-triangulation of a point set, and show that the pseudo-triangulation changes only quadratically many times if points move along algebraic arcs of constant degree. In addition, by refining the pseudotriangulation, we show triangulations of points that only change about O(n7/3 ) times for linear motion. We then describe an algor...

• Type: Journal
• Year: 2002
• Where: IJRR
• Authors: Pankaj K. Agarwal, Julien Basch, Leonidas J. Guibas, John Hershberger, Li Zhang
• Keywords: Bounding Volume Hierarchies, IJRR 2002, Kinetic Data Structure, Polygons