Zubair Khalid

Academic Webpage

Research School of Engineering
College of Engineering and Computer Science
The Australian National University

Software - Computing exact closed-form distance distributions in polygon regions


This software computes: (i) the exact closed-form probability density function and (ii) the exact closed-form cumulative density function of the distance between a randomly located node and any arbitrary reference point inside a regular L-sided polygon. These results can be used to obtain the closed-form probability density function of the Euclidean distance between any arbitrary reference point and its nth neighbor node when N nodes are uniformly and independently distributed (i.e. according to a uniform Binomial Point Process) inside a regular L-sided polygon. These distance distributions have many applications in wireless networks.


This code is available in both Mathematica and Matlab (Released: May 2013):

Relevant Paper:

  • Z. Khalid and Salman Durrani, “Distance distributions in regular polygons,” IEEE Trans. Veh. Tech., vol. 62, no. 5, pp. 2363-2368, June 2013. (pdf)

More details and the application of the distance distributions are available here.