Monte-Carlo simulation of the chord length distribution function across convex bodies, non-convex bodies and random media

The study of chord length distributions across various kinds of geometrical shapes, including stochastic mixtures, is a topic of great interest in many research fields ranging from ecology to neutronics. We have tried here to draw links between theoretical results and actual simulations for simple objects like disks, circular rings, spheres, hollow spheres, as well as for random media consisting of stochastic mono- or polydisperse spheres packing (three different packing algorithms were tested). The Monte Carlo simulations which were performed for simple objects fit perfectly theoretical formulas. For stochastic binary mixtures the simulations were still in rather good agreement with known analytical results.