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Efficient Collision Detection among Moving Spheres with Unknown

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Efficient Collision Detection among Moving Spheres with Unknown Powered By Docstoc
					CS 780


Efficient Collision Detection
among Moving Spheres with
    Unknown Trajectories

           Ho Kyung Kim
         Leonidas J. Guibas
          Sung Yong Shin
             2004. 5. 17
                 Outline
•   Introduction
•   Related Work
•   Time-Varying Bound
•   Collision Detection among TVBs
    – Event-driven approach
    – Events for Time-Varying Bounds
• Results
• Conclusion
            Introduction
• Issues on collision detection
  – Reduce the number of comparisons
  – Make the shape of the objects simple
  – Catch all collisions without missing


• How to solve?
  – Space Subdivision
  – Time-varying bound
  – Event-driven approach
             Related Work
• Polyhedral object with ballistic trajectories
  – [Mirtich 96], [Mirtich 97]
• Event-driven approach
  – [Kim et al. 98]
• Kinetic data structure
  – [Basch et al. 99], [Guibas 98]
• Unknown trajectory with maximum norm of
  acceleration
  – [Hayward et al. 95], [Hubbard 94], [Hubbard
    95]
     Time-Varying Bound
• Assumption :
     Event-Driven Approach
• Subspace tree
  – Maintains the list of spheres
   in each subspace
• Event tree
  – Maintains the candidate events
   of each sphere
• The earliest event actually occurs, and
  subspace and event trees are modified.
• Hierarchical space subdivision
• Cost model
   Events for Time-Varying
           Bounds
• Entering/Leaving event




  – Diameter of B(si) is bounded by the side length
    of a subspace
  – # of non-empty subspace is O(n)
  – # of time-varying bounds intersecting a
    subspace is O(1)
   Events for Time-Varying
           Bounds
• Resetting event


                    →

• Colliding event
    Events for Time-Varying
            Bounds
• Complexity analysis
   – For each B(si),
      • # of candidate entering/leaving events : O(1)
      • # of candidate colliding events : O(1)
      • # of resetting event : 1
   – Total number of candidate events for the TVB in the
     event tree is O(n)
   – Handling an event : O(log n) (regardless of its type)

   – Detection of all collisions among the spheres during the
     time interval : O(ntlog n + nclog n)
• Efficiency improvement
   – Do not insert into the event tree the candidate events of
     B(si), whose event times are later than that of its
     resetting event
                Results
• Event time calculation



  – Entering/Leaving :
  – Resetting :          →
  – Colliding :

  – Collision with a face of the box
                 Results
• Performance
  – Average processing time(2003)
                Results
– Comparison with Hubbard’s algorithm




– # of actual events
             Conclusion
• New algorithm which can detect
  collisions efficiently
  – Time-varying bound
  – Generalization of the event-driven
    approach
  – Interactive rate
• Future work
  – Apply to various applications such as
    crowd simulation

				
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posted:9/15/2012
language:English
pages:13