Lines through Segments in 3D Space

Fogel, Efi; Hemmer, Michael; Porat, Amir; Halperin, Dan

doi:10.1007/978-3-642-33090-2_40

Cited by 2 publications

(2 citation statements)

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“…Some three-dimensional variants have also been studied, most notably the problem of computing stabbers or transversals of a set of segments in 3D [9,13,22] and a few stabbing problems for convex polyhedra [9,27,33] .…”

Section: Previous Workmentioning

confidence: 99%

“…Several papers [32,25,34,12,30,31,19] have studied problem variants with the goal of optimizing perimeter or area of the convex polygon stabbing a set of segments, using criteria (ii) and (iii). Some three-dimensional variants have also been studied, most notably the problem of computing stabbers or transversals of a set of segments in 3D [9,13,22] and a few stabbing problems for convex polyhedra [9,27,33] .…”

Section: Previous Workmentioning

confidence: 99%

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Stabbing segments with rectilinear objects

Aguas

Garijo

Korman

et al. 2017

Applied Mathematics and Computation

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Abstract. Given a set S of n line segments in the plane, we say that a region R ⊆ R 2 is a stabber for S if R contains exactly one endpoint of each segment of S. In this paper we provide optimal or near-optimal algorithms for reporting all combinatorially different stabbers for several shapes of stabbers. Specifically, we consider the case in which the stabber can be described as the intersection of axis-parallel halfplanes (thus the stabbers are halfplanes, strips, quadrants, 3-sided rectangles, or rectangles). The running times are O(n) (for the halfplane case), O(n log n) (for strips, quadrants, and 3-sided rectangles), and O(n 2 log n) (for rectangles).

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