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A box-tree is a bounding-volume hierarchy that uses axis-aligned boxes as bounding volumes. We describe a new algorithm to construct a box-tree for a 3D scene consisting of n objects, and we analyze its worst-case query time for approximate range queries. If the input scene has certain characteristics that we derived from our application---collision detection in industrial installations---then the query times are polylogarithmic, not only for searching with boxes but also for range searching with other constant-complexity ranges.

Box-trees for collision checking in industrial installations