  Distance distributions are a key building block in stochastic geometry
modelling of wireless networks and in many other fields in mathematics and
science. In this paper, we propose a novel framework for analytically computing
the closed form probability density function (PDF) of the distance between two
random nodes each uniformly randomly distributed in respective arbitrary
(convex or concave) polygon regions (which may be disjoint or overlap or
coincide). The proposed framework is based on measure theory and uses polar
decomposition for simplifying and calculating the integrals to obtain closed
form results. We validate our proposed framework by comparison with simulations
and published closed form results in the literature for simple cases. We
illustrate the versatility and advantage of the proposed framework by deriving
closed form results for a case not yet reported in the literature. Finally, we
also develop a Mathematica implementation of the proposed framework which
allows a user to define any two arbitrary polygons and conveniently determine
the distance distribution numerically.
