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Mathematica and Matlab Software for Computing Distance Distributions

During the course of my research, I have written a number of software libraries in collaboration with my students. One of them is now available publicly here and others will be made available in the future.

If you use the software in your research, please reference our relevant publication (see details below).

If you have any suggestions for improving the software, please email me and we can incorporate this in the software.

  • Computing distance distributions between two random points, each uniformly randomly distributed in arbitrary convex polygon regions [Released: TBA]
    • Mathematica code
    • Our paper
    • Computing distance distributions in K-tier heterogeneous networks with arbitrary reference point [Released: coming soon!]
      In K-tier heterogeneous networks, the coverage regions are modelled using a multiplicatively weighted Voronoi diagram. 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 or outside an arbitrarily shaped multiplicatively weighted Voronoi cell.
      • Matlab code (zipped): Developed and tested [Nov. 2014].
      • Mathematica code
      • Our paper is still in draft form and I am aiming to write it up in the second half of this year.
      • Screen shot:

    • Computing exact closed-form distance distributions in arbitrary (convex or concave) polygon regions with arbitrary reference point [Released: June 2015]
      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 or outside an arbitrary (concave or convex) polygon.
    • Computing exact closed-form distance distributions in arbitrary convex polygon regions with interior reference point
      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 an arbitrary L-sided convex polygon.
    • Computing exact closed-form distance distributions in regular polygon regions with interior reference point [Released: May 2013]
      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.


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Author: Salman Durrani.
Last Updated: 9 June, 2017.