Set operations on polyhedra using binary space partitioning trees
SIGGRAPH '87 Proceedings of the 14th 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
Optimal binary space partitions for orthogonal objects
Journal of Algorithms
Approximation algorithms for geometric tour and network design problems (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
New results on binary space partitions in the plane
Computational Geometry: Theory and Applications
Self-customized BSP trees for collision detection
Computational Geometry: Theory and Applications - special issue on virtual reality
Binary Space Partitions for Fat Rectangles
SIAM Journal on Computing
Binary space partitions for axis-paralles line segments: size-height tradeoffs
Information Processing Letters
Binary Space Partitions for Line Segments with a Limited Number of Directions
SIAM Journal on Computing
Linear Size Binary Space Partitions for Fat Objects
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Nearly optimal expected-case planar point location
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On visible surface generation by a priori tree structures
SIGGRAPH '80 Proceedings of the 7th annual conference on Computer graphics and interactive techniques
Guarding scenes against invasive hypercubes
Computational Geometry: Theory and Applications
Binary Space Partitions for Axis-Parallel Segments, Rectangles, and Hyperrectangles
Discrete & Computational Geometry
Binary Space Partitions of Orthogonal Subdivisions
SIAM Journal on Computing
Approximate range searching using binary space partitions
Computational Geometry: Theory and Applications
Computational Geometry: Algorithms and Applications
Computational Geometry: Algorithms and Applications
Binary Space Partitions for Axis-Aligned Fat Rectangles
SIAM Journal on Computing
Shooting permanent rays among disjoint polygons in the plane
Proceedings of the twenty-fifth annual symposium on Computational geometry
Shooting permanent rays among disjoint polygons in the plane
Proceedings of the twenty-fifth annual symposium on Computational geometry
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A binary space partition (BSP) for a set of disjoint objects in Euclidean space is a recursive decomposition, where each step partitions the space (and some of the objects) along a hyperplane and recurses on the objects clipped in each of the two open halfspaces. The size of a BSP is defined as the number of resulting fragments of the input objects. It is shown that every set of n disjoint line segments in the plane admits a BSP of size O(n log n / log log n). This bound is best possible apart from the constant factor.