Random networks in configuration space for fast path planning
Random networks in configuration space for fast path planning
Realistic input models for geometric algorithms
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Balanced aspect ratio trees: combining the advantages of k-d trees and octrees
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Computational Geometry: Theory and Applications
Box-trees and R-trees with near-optimal query time
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Balanced aspect ratio trees
Local polyhedra and geometric graphs
Proceedings of the nineteenth annual symposium on Computational geometry
The Priority R-tree: a practically efficient and worst-case optimal R-tree
SIGMOD '04 Proceedings of the 2004 ACM SIGMOD international conference on Management of data
Local polyhedra and geometric graphs
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
Approximate range searching using binary space partitions
Computational Geometry: Theory and Applications
The priority R-tree: A practically efficient and worst-case optimal R-tree
ACM Transactions on Algorithms (TALG)
Approximate range searching using binary space partitions
Computational Geometry: Theory and Applications
Local polyhedra and geometric graphs
Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003
A dynamic bounding volume hierarchy for generalized collision detection
Computers and Graphics
Approximate range searching in external memory
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Efficient c-oriented range searching with DOP-trees
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Approximate range searching using binary space partitions
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
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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.