Orientation-dependent section distributions for convex bodies

Abstract

In the paper the orientation dependent chord length distribution functions for some bounded convex domains are obtained. In particular, formulae for the orientation dependent chord length distributions for a regular polygon and an ellipse are obtained. Explicit forms of the orientation dependent chord length distributions were known only in the cases of a disc and a triangle. We also obtain the cross-section area distribution functions for an ellipsoid and a cylinder. The cross-section area distribution function was known only in the case of a ball.