Recognizing an envelope of lines in linear time

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Abstract

The envelope polygon of a set of lines, L, is the polygon consisting of the finite length segments that hound the infinite faces of the arrangement A(L). Given an envelope polygon, we show how to sort its edges by slope in linear time. Using this result, we can determine whether a given polygon P is an envelope in linear time.

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Guévremont, E., & Snoeyinkt, J. (1992). Recognizing an envelope of lines in linear time. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 650 LNCS, pp. 370–377). Springer Verlag. https://doi.org/10.1007/3-540-56279-6_89

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