We present an algorithm that, given a set of n parallel line segments in the plane, finds a convex polygon whose boundary intersects each segment at least once, or determines that none exists. Our algorithm runs in O(n log n) steps and linear space, which is optimal. Our solution involves a reduction to a bipartite stabbing problem, using a “point-sweeping” or “chain-unwrapping” technique. We use geometric duality to solve bipartite stabbing.
CITATION STYLE
Goodrich, M. T., & Snoeyink, J. S. (1989). Stabbing parallel segments with a convex polygon. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 382 LNCS, pp. 231–242). Springer Verlag. https://doi.org/10.1007/3-540-51542-9_21
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