Finding a line transversal of axial objects in three dimensions
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
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An algorithm is presented for determining in O(n log n) time whether there exists a line that stabs each of n polygons whose edges are from three sets of parallel lines. Using this algorithm, one can determine in O(n log n) time whether there exists a line that stabs each of n isothetic boxes or rectangles. If any stabbing line exists, the algorithm computes and returns one such stabbing line.