INTERSECTIONS OF RANDOM LINE SEGMENTS
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Published:1994-09
Issue:03
Volume:04
Page:261-274
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ISSN:0218-1959
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Container-title:International Journal of Computational Geometry & Applications
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language:en
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Short-container-title:Int. J. Comput. Geom. Appl.
Affiliation:
1. School of Computer Science, McGill University, Montreal, Quebec H3A 2A7, Canada
Abstract
We consider a random collection of n line segments, in which the segments are independently drawn by picking the midpoint according to a given distribution in the plane, by picking a uniformly distributed random direction, and by adding an independently sampled segment length. We study the expected behavior of the number of intersections as a function of n, the lengths of the line segments, and the distribution of the midpoints. This includes a universally applicable law of large numbers.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science
Cited by
2 articles.
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