Distance Distributions in Regular Polygons
This paper derives the exact cumulative density function of the distance between a randomly located node and any arbitrary reference point inside a regular L-sided polygon. Using this result, the authors obtain the closed-form Probability Density Function (PDF) of the Euclidean distance between any arbitrary reference point and its n-th neighbour node, when N nodes are uniformly and independently distributed inside a regular L-sided polygon. First, they exploit the rotational symmetry of the regular polygons and quantify the effect of polygon sides and vertices on the distance distributions. Then, they propose an algorithm to determine the distance distributions given any arbitrary location of the reference point inside the polygon.