
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 (concave or convex) polygons with or without holes [Released: Jan. 2021]
 Mathematica Notebooks:
 Example 1: Abritrary polygons without holes. Requires Mathematica 11 or higher version.
 Example 2: Abritrary polygons with holes. Requires Mathematica 12.
 Our paper is currently under review in Mathematical Methods in Applied Sciences journal (revised: 24 Jan. 2021)
 Screenshot:
 Computing distance distributions in arbitrary (convex or concave) polygon regions with holes and arbitrary reference point [Released: coming soon!]
In Ktier heterogeneous networks, the coverage regions are modelled using a multiplicatively weighted Voronoi diagram. This software computes: (i) the exact closedform probability density function and (ii) the exact closedform 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 hoping to write it up in the second half of this year.
 Screen shot:
 Computing exact closedform distance distributions in arbitrary (convex or concave) polygon regions without holes and arbitrary reference point [Released: June 2015]
This software computes: (i) the exact closedform probability density function and (ii) the exact closedform 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 closedform distance distributions in arbitrary convex polygon regions with interior reference point
This software computes: (i) the exact closedform probability density function and (ii) the exact closedform cumulative density function of the distance between a randomly located node and any arbitrary reference point inside an arbitrary Lsided convex polygon.
 Computing exact closedform distance distributions in regular polygon regions with interior reference point [Released: May 2013]
This software computes: (i) the exact closedform probability density function and (ii) the exact closedform cumulative density function of the distance between a randomly located node and any arbitrary reference point inside a regular Lsided polygon. These results can be used to obtain the closedform 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 Lsided polygon. These distance distributions have many applications in wireless networks. This code is available in both Mathematica and Matlab.
