Hybrid Bounding Volumes for Distance Queries Distance Query

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

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.

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

BV Comparison

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.

A class of similar BV’s

Cost of distance computation

Demo

Benchmarks Small torus passes through center of large torus

Benchmarks Small torus passes through center of very large torus

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

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.