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
Binary Space Partitions for Fat Rectangles
SIAM Journal on Computing
Multidimensional binary search trees used for associative searching
Communications of the ACM
Binary space partitions for 3D subdivisions
SODA '03 Proceedings of the fourteenth 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
Efficient hidden-surface removal in theory and in practice
Efficient hidden-surface removal in theory and in practice
Binary Space Partitions for Axis-Parallel Segments, Rectangles, and Hyperrectangles
Discrete & Computational Geometry
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We consider the problem of constructing binary space partitions (BSPs) for orthogonal subdivisions (space filling packings of boxes) in d-space. We show that a subdivision with n boxes can be refined into a BSP of size O(n d+1/3), for all d ≥ 3, and that such a partition can be computed in time O(K log n), where K is the size of the BSP produced. Our upper bound on the BSP size is tight for 3-dimensional subdivisions in higher dimensions, this is the first nontrivial result for general full-dimensional boxes. We also present a lower bound construction for a subdivision of n boxes in d-space that requires a BSP of size Ω(n946;(d)), where β(d) converges to (1+ √5 )/2 as d → ∞.