Summary: ALGORITHMS FOR LINE TRANSVERSALS IN SPACE
School of Computer Science
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Algorithms are developed for determining if a set of polyhedral
objects in R 3 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 ver
tices, we give a O(n 5 ) algorithm for determining the existence of, and
computing, a line transversal. Hellytype 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