Hybrid Bounding Volumes for Distance Queries

1
Hybrid Bounding Volumes for Distance Queries

• Distance Query returns the minimum distance
  between two geometric models
• Major application is path planning - in some
  methods, 90 of execution time spent in distance
  queries

2
Hierarchical Method

• With polygonal models, must find pair of
  triangles with minimum distance
• Bounding volumes accelerate this task
• when distance between tris computed, minimum is
  adjusted
• if a pair of BVs are farther apart than current
  minimum, the triangles they contain cannot
  achieve a minimum.

3
Use of BVs
current minimum
Can reject all pairs within the BVs
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BV Comparison
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Hybrid BVs

• Use a simpler BV when it prunes search equally
  well - benefit from lower cost of BV distance
  computation.
• Complications
• deciding which BV to use - dynamically or
  statically
• optimizing distance computation between all pairs
  of BVs in tree.

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A class of similar BVs
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Cost of distance computation
8
Demo
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Benchmarks
Small torus passes through center of large torus
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Benchmarks
Small torus passes through center of very large
torus
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Contributions

• A class of shapes which might have good
  properties for hybrid hierarchies.
• Distance algorithm for a pair of rectangles.

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Future work

• Characterize situations where RSSs are not the
  optimal BV type for distance.
• Determine how to detect these situations so that
  other BVs can be used.