Orientation-Dependent Distribution of the Length of a Random Segment andn Covariogram

摘要

The paper considers a random segment L(omega) in R-n with fixed direction and length that intersects a given bounded convex body D subset of R-n. We obtain a relationship between the covariogram of D and the distribution of the random variable vertical bar L vertical bar - the length of L boolean AND D. A relationship between the distribution of vertical bar L vertical bar and the orientation-dependent chord length distribution is also obtained. As a consequence, we obtain a relationship between