Distance distributions in regular polygons

Zubair Khalid, Salman Durrani

    Research output: Contribution to journalArticlepeer-review

    71 Citations (Scopus)

    Abstract

    This paper derives the exact cumulative density function (cdf) of the distance between a randomly located node and any arbitrary reference point inside a regular L-sided polygon. Using this result, we 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 inside a regular L-sided polygon. First, we exploit the rotational symmetry of the regular polygons and quantify the effect of polygon sides and vertices on the distance distributions. Then, we propose an algorithm to determine the distance distributions, given any arbitrary location of the reference point inside the polygon. For the special case when the arbitrary reference point is located at the center of the polygon, our framework reproduces the existing result in the literature.

    Original languageEnglish
    Article number6415342
    Pages (from-to)2363-2368
    Number of pages6
    JournalIEEE Transactions on Vehicular Technology
    Volume62
    Issue number5
    DOIs
    Publication statusPublished - 2013

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