Collision Detection for Interactive Graphics Applications

1
Collision Detection for Interactive Graphics
Applications
CS780

• Philip M. Hubbard

2004. 5. 12 ???
2
Outline

• Introduction
• Related Work
• Overview
• Space-Time Bounds
• Space-Time Bound Intersections
• Pairwise Collision Detection
• Experimental Results
• Conclusions

3
Introduction

• Collision detection
• Interactive applications
• Real-time performance
• Tolerating user-guided motions
• Goals
• Rigid or articulated objects
• Allowing progressive refinement interrupt

4
Related Work

• Basic algorithm

5
Related Work

• Fixed-timestep weakness
• Canny86, Duff92, Snyder93
• Cully86, Foisy90, Lin93
• All-pairs weakness
• Moore88, Shaffer92, Smith95
• Turk90
• Pair-processing weakness
• Thibault87, Garcia-Alonso95, Sclaroff91

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Motivation

• Space-time bounds
• 4D structures with a time dimension
• Broad phase
• Finding a candidate pair of colliding objects
• Sphere tree
• Hierarchical approximation of an object
• Narrow phase
• Collision check between a pair of candidate
  objects

7
Overview
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Space-Time Bounds

• Definitions
• O a point object
• position, velocity,
  and acceleration at time t
• Assumptions
• known at t 0, but not
  future

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Space-Time Bounds

• Assertion
• 
  (1)
• A parabolic horn

10
Space-Time Bounds

• The O redefined
• r a radius of a bounding sphere
• A 4D hypertrapezoid T
• Easy to check collision

11
Space-Time Bounds

• A 4D cutting plane P
• When acceleration direction is constrained
• (2)

12
Space-Time Bound Intersections

• Three possible intersections
• Two hypertrapezoid faces
• One face and one cutting plane
• Two cutting planes

13
Space-Time Bound Intersections

• Face-face intersections
• If two hypertrapezoids, T1 and T2, intersect for
  the first time at ti, there must be an
  intersection at ti between faces in the same Fa

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Space-Time Bound Intersections

• The projection method

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Space-Time Bound Intersections

• The projection method

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Space-Time Bound Intersections

• The projection method
• Considering cutting planes
• Bentley-Ottmann algorithm
• But, typically

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Space-Time Bound Intersections

• The subdivision method
• Similar to 4D octree
• Subdividing the space until nb faces remained

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Space-Time Bound Intersections

• Comparision

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Space-Time Bound Intersections

• Face-plane intersections
• Intersection between f1 and P2
• Intersection between p1 and P2
• Direction of a line of intersection
• Points on the intersection
• Half-space testing

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Space-Time Bound Intersections

• Plane-plane intersections
• Same to the face-plane case
• Involving 12 half-spaces

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Pairwise Collision Detection

• A pair of objects
• At a specific time
• Sphere-trees
• Small runtime overhead
• Allowing interrupts

22
Sphere Tree Construction

• Simulated annealing
• Accurate
• Irregular distributions of spheres slow
• Medial-axis surfaces
• Coverage not guaranteed

23
Experimental Results

• Comparison with Turks BSP tree

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Experimental Results
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Experimental Results
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Conclusions

• A time-critical approach to collision detection
• Future work
• Interframe coherence
• Considering velocity and position
• Making broad phase interruptible
• Parallel processing

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The Broad Phase