Properties of chord length distributions of nonconvex bodies

Cauchy's formula which relates the mean chord length (isotropic uniform random chords) of a convex body in R-n with its volume and surface is extended to the case of nonconvex bodies in the framework of integral geometry. This allows us to generalize the extended Cauchy's formula recently discovered by Blanco and Fournier [Europhys. Lett. 61 (2), 168 (2003)], in the field of diffusive random walks, to nonconvex bodies. Monte Carlo simulations illustrate these points in R-2 and in R-3. (C) 2003 American Institute of Physics.