Deformable free-space tilings for kinetic collision detection

Journal Article

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 (n7/3) 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.

Full Text

Duke Authors

Cited Authors

  • Agarwal, PK; Basch, J; Guibas, LJ; Hershberger, J; Zhang, L

Published Date

  • March 1, 2002

Published In

Volume / Issue

  • 21 / 3

Start / End Page

  • 179 - 197

International Standard Serial Number (ISSN)

  • 0278-3649

Digital Object Identifier (DOI)

  • 10.1177/027836402320556395

Citation Source

  • Scopus