Collision detection is a problem that has often been addressed efficiently with the use of hierarchical culling data structures. In the subproblem of self-collision detection for triangle meshes, however, such hierarchical data structures lose much of their power, because triangles adjacent to each other cannot be distinguished from actually colliding ones unless individually tested. Shape regularity of surface patches, described in terms of orientation and contour conditions, was proposed long ago as a culling criterion for hierarchical self-collision detection. However, to date, algorithms based on shape regularity had to trade conservativeness for efficiency, because there was no known algorithm for efficiently performing 2D contour self-intersection tests. In this paper, we introduce a star-contour criterion that is amenable to hierarchical computations. Together with a thorough analysis of the tree traversal process in hierarchical self-collision detection, it has led us to novel hierarchical data structures and algorithms for efficient yet conservative self-collision detection. We demonstrate the application of our algorithm to several example animations, and we show that it consistently outperforms other approaches.

@Article\{SPO10,
  author       = "Schvartzman, Sara C. and Perez, Alvaro G. and Otaduy, Miguel A.",
  title        = "Star-Contours for Efficient Hierarchical Self-Collision Detection",
  journal      = "ACM Trans. on Graphics (Proc. of ACM SIGGRAPH)",
  number       = "3",
  volume       = "29",
  year         = "2010",
  url          = "http://gmrv.es/Publications/2010/SPO10"
}