Some properties of line segment processes
Keyword(s):
This paper formulates the random process of line-segments in the Euclidean plane. Under conditions more general than Poisson, expressions are obtained, for Borel A ⊂ R2, for the first moments of M(A), the number of segment mid-points in A; N(A), the number of segments which intersect with convex A; S(A), the total length within A of segments crossing A; and C(A) the number of segment-segment crossings within A. In the case of Poisson mid-points, the distribution of the rth nearest line-segment to a given point is found.
1976 ◽
Vol 13
(01)
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pp. 96-107
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2013 ◽
Vol 23
(06)
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pp. 443-459
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2012 ◽
Vol 21
(06)
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pp. 1250059
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2013 ◽
Vol 05
(03)
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pp. 1350021
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2017 ◽
Vol 27
(03)
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pp. 159-176
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2011 ◽
pp. 14-23
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1978 ◽
Vol 15
(03)
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pp. 494-501
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1975 ◽
Vol 27
(3)
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pp. 636-665
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