On generalized buffon needle problem for lattices

Two new concepts, the generalized support function and restricted chord function, both referring to a convex set, were introduced in [1]. General formulae to yield the kinematic measure of a segment of fixed length in a convex set were established based on these concepts. In this article, using the partial intersection method, we consider the generalized Buffon problem for three kinds of lattices. We determine the probability of intersection of a body test needle of length l, l < α.