Pankaj K. Agarwal, Duke University, Durham, NC
Julien Basch, Stanford University, Stanford, CA
Leonidas J. Guibas, Stanford University, Stanford, CA
John Hershberger, Mentor Graphics Corp., Wilsonville, OR
Li Zhang, Stanford University, Stanford, CA

We present kinetic data structures for detecting collisions between a set of polygons that are moving continuously in the plane. 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 pseudo-triangulations using the framework of kinetic data structures, and analyze their performance. Specifically, we first describe an algorithm for maintaining a pseudo-triangulation of a point set, and show that this pseudo-triangulation changes only quadratically many times if points move along algebraic arcs of constant degree. We then describe an algorithm for maintaining a pseudo-triangulation of a set of convex polygons. Finally, we extend our algorithm to the general case of maintaining a pseudo-triangulation of a set of moving simple polygons. These methods can be extended to situations where the polygons deform as well as move.