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- W1981127926 abstract "Algorithms are developed for determining if a set of polyhedral objects in R3 can be intersected by a common transversal (stabbing) line. It can be determined in O(n) time if a set of n lines in space has a line transversal, and such a transversal can be found in the same time bound. For a set of n line segments, the complexity of finding such a transversal becomes O(nlogn). Finally, for a set of polyhedra with a total of n vertices, we give a O(n5) algorithm for determining the existence of, and computing, a line transversal. Helly-type theorems for lines and segments are also given. In particular, it is shown that if every six of a set of lines in space are intersected by a common transversal, then the entire set has a common transversal." @default.
- W1981127926 created "2016-06-24" @default.
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- W1981127926 date "1987-01-01" @default.
- W1981127926 modified "2023-09-26" @default.
- W1981127926 title "Algorithms for line transversals in space" @default.
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- W1981127926 doi "https://doi.org/10.1145/41958.41990" @default.
- W1981127926 hasPublicationYear "1987" @default.
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