CHORD LENGTH DISTRIBUTIONS AND RELATED QUANTITIES FOR SPHEROIDS
The chord length distributions are derived that result when spheroids are randomly traversed by straight lines. The first part of the article applies generally to convex domains in three-dimensional space; the relationships between the chord length distributions and their moments for different types of randomness are summarized. Subsequently the chord length distributions, the point pair distance distributions, and the geometric reduction factors are derived by a suitable transformation from the distributions for the sphere. All integrals can be resolved and the resulting formulae are valid for both prolate and oblate spheroids. The moments of the chord length distributions are obtained by the same transformation from those for the sphere. The solutions for ellipses are given in the Appendix and contain Legendre integrals.
Bibliographic Reference: RADIATION RESEARCH, VOL. 98 (1984), NO. 3, PP. 425-437.
Record Number: 1989123031200 / Last updated on: 1987-01-01
Available languages: en