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
Optimal binary space partitions for orthogonal objects
Journal of Algorithms
On the optimal binary plane partition for sets of isothetic rectangles
Information Processing Letters
Perfect binary space partitions
Computational Geometry: Theory and Applications - Special issue: computational geometry, theory and applications
New results on binary space partitions in the plane
Computational Geometry: Theory and Applications
Improved approximation algorithms for rectangle tiling and packing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A note on binary plane partitions
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
On the Exact Size of the Binary Space Partitioning of Sets of Isothetic Rectangles with Applications
On the Exact Size of the Binary Space Partitioning of Sets of Isothetic Rectangles with Applications
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
Binary space partitions for axis-paralles line segments: size-height tradeoffs
Information Processing Letters
Binary space partitions for 3D subdivisions
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
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We provide a variety of new results, including upper and lower bounds, as well as simpler proof techniques for the efficient construction of binary space partitions (BSP's) of axis-parallel segments, rectangles, and hyperrectangles. (a) A consequence of the analysis in \cite{dAF} is that any set of $n$ axis-parallel and pairwise-disjoint line segments in the plane admits a binary space partition of size at most $2n-1$. We establish a worst-case lower bound of $2n-o(n)$ for the size of such a BSP, thus showing that this bound is almost tight in the worst case. (b) We give an improved worst-case lower bound of $\frac{9}{4}n-o(n)$ on the size of a BSP for isothetic pairwise disjoint rectangles. (c) We present simple methods, with equally simple analysis, for constructing BSP's for axis-parallel segments in higher dimensions, simplifying the technique of \cite{PY2} and improving the constants. (d) We obtain an alternative construction (to that in \cite{PY2}) of BSP's for collections of axis-parallel rectangles in 3-space. (e) We present a construction of BSP's of size $O(n^{5/3})$ for $n$ axis-parallel pairwise disjoint 2-rectangles in $\reals^4$, and give a matching worst-case lower bound of $\Omega(n^{5/3})$ for the size of such a BSP. (f) We extend the results of \cite{PY2} to axis-parallel $k$-dimensional rectangles in $\reals^d$, for $k