The Distributions of Measures of Visibility on Line Segments in Three Dimensional Spaces under Poisson Shadowing Processes

摘要

The problem of determining the moments of visibility measures on star-shaped curves, under Poisson random shadowing process in the plane (see 4) is generalized here to the problem of determining the moments of visibility measures on line segments in a three-dimensional space, when the shadowing process is created by a Poisson random field of spheres of random size. The present paper provides the methodology for reducing the three-dimensional problem to a two-dimensional one, and employing the general theory of 4 to solve the present problem. Although the general approach is similar, the functions derived in the present paper are somewhat different fo the sake of simplifying the computations. (Author)