Approximate range searching using binary space partitions
Computational Geometry: Theory and Applications
Shooting permanent rays among disjoint polygons in the plane
Proceedings of the twenty-fifth annual symposium on Computational geometry
Binary plane partitions for disjoint line segments
Proceedings of the twenty-fifth annual symposium on Computational geometry
Approximate range searching using binary space partitions
Computational Geometry: Theory and Applications
Determining the visibility of a planar set of line segments in O(n log log n) time
ICCSA'07 Proceedings of the 2007 international conference on Computational science and Its applications - Volume Part II
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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We show that there is always a binary space partition (BSP) of size O(n log k) and an autopartition of size O(nk) for n disjoint line segments in the plane, assuming that the segments have k distinct orientations. In particular, if k is a constant, these bounds imply that there is a linear-size BSP and autopartition. Our proof is constructive and can be turned into algorithms computing such a BSP or autopartition in O(n2) and O(n2k) times.