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Volume 21 Issue 03 - Publication Date: 1 March 2002
 
Deformable Free-Space Tilings for Kinetic Collision Detection
 
Pankaj K. Agarwal Center for Geometric Computing, Department of Computer Science, Duke University, USA , Julien Basch and Leonidas J. Guibas Computer Science Department, Stanford University, USA , John Hershberger Mentor Graphics Corp., USA and Li Zhang Computer Science Department, Stanford University, USA
 
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 pseudo-triangulations 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 pseudo-triangulation, we show triangulations of points that only change about O(n 7 3 ) times for linear motion. 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 or deforming simple polygons.
 
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