Class #4: Collision Detection (1/2) –
            Hierarchical Methods

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The figure on the left shows a scene in which objects are modeled using several dozen thousand triangles. Hierarchical methods quickly prune out pairs of triangles that are too far apart to intersect. The image in the middle shows a “triangulated cat” and a subset of the sphere hierarchy used to approximate this model at successive levels (1st required paper). The figure on the right illustrates the need for “dynamic” collision checking (2nd required paper)

  • Topics:
    - Role of collision detection and distance computation in motion planning
    - Bounding Volume Hierarchy (BVH) approach
    - Static vs. dynamic collision checking
    - Fixed vs. adaptive bisection in dynamic collision checking
  • Required Readings:
    • Bounding Volume Hierarchy (with spheres):
      S. Quinlan. Efficient Distance Computation Between Non-Convex Objects. Proc. IEEE Int. Conf. on Robotics and Automation, 1994. [pdf]
    • Adaptive bisection in dynamic collision checking
      F. Schwarzer, M. Saha, J.C. Latombe. Adaptive Dynamic Collision Checking for Single and Multiple Articulated Robots in Complex Environments, manuscript, 2003. [ps] [pdf]

  • Other Readings:
    • The PQP collision checker (BVH approach with Oriented Bounding Boxes):
      S. Gottschalk, M. Lin, and D. Manocha. OBB-Tree: A Hierarchical Structure for Rapid Interference Detection. Proc. ACM SIGGRAPH '96, 1996. [pdf]
    • Combination of BVH, interval arithmetics, and polynomial techniques:
      S. Redon, A. Kheddar and S. Coquillart. Fast Continuous Collision Detection between Rigid Bodies. Proc. Eurographics, Sept. 2002. [pdf]
    • See also Ming Lin's webpage for numerous references and downloadable software.

  • Powerpoint slides:

o       Introduction

o       Paper 1  

o       Paper 2