Convex partitions of polyhedra: a lower bound and worst-case optimal algorithm
SIAM Journal on Computing
Set operations on polyhedra using binary space partitioning trees
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Near real-time shadow generation using BSP trees
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
Efficient binary space partitions for hidden-surface removal and solid modeling
Discrete & Computational Geometry - Selected papers from the fifth annual ACM symposium on computational geometry, Saarbrücken, Germany, June 5-11, 1989
Merging BSP trees yields polyhedral set operations
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Optimal binary space partitions for orthogonal objects
Journal of Algorithms
Fast object-precision shadow generation for area light sources using BSP trees
I3D '92 Proceedings of the 1992 symposium on Interactive 3D graphics
New results on binary space partitions in the plane
Computational Geometry: Theory and Applications
Binary space partitions for axis-parallel segments, rectangles, and hyperrectangles
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
A note on binary plane partitions
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Slice and dice: a simple, improved approximate tiling recipe
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Binary space partitions for line segments with a limited number of directions
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
On visible surface generation by a priori tree structures
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
Binary space partitions of orthogonal subdivisions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
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We consider the following question: Given a subdivision of space into n convex polyhedral cells, what is the worst-case complexity of a binary space partition (BSP) for the subdivision? We show that if the subdivision is rectangular and axis-aligned, then the worstcase complexity of an axis-aligned BSP is Ω(n4/3) and O(nα log2 n), where α = 1 + log2(4/3 ) = 1.4150375 .... By contrast, it is known that the BSP of a collection of n rectangular cells not forming a subdivision has worstcase complexity Θ(n3/2). We also show that the worstcase complexity of a BSP for a general convex polyhedral subdivision of total complexity O(n) is Ω(n3/2).