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 BV’s are farther apart than current minimum, the triangles they contain cannot achieve a minimum.

3. Use of BV’s current minimum Can reject all pairs within the BV’s

4. BV Comparison

5. Hybrid BV’s • 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 BV’s in tree.

6. A class of similar BV’s

7. Cost of distance computation

8. Demo

9. Benchmarks Small torus passes through center of large torus

10. Benchmarks Small torus passes through center of very large torus

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

12. Future work • Characterize situations where RSS’s are not the optimal BV type for distance. • Determine how to detect these situations so that other BV’s can be used.