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A NOTE CONCERNING THE DISTANCES OF UNIFORMLY DISTRIBUTED POINTS FROM THE CENTRE OF A RECTANGLE

Part of: Geometric probability and stochastic geometry

Published online by Cambridge University Press:  07 June 2012

ROBERT STEWART  and
HONG ZHANG
ROBERT STEWART*
Affiliation:
Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada T6G 2E8 (email: RLStewart@ieee.org)
HONG ZHANG
Affiliation:
Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada T6G 2E8 (email: hzhang@ualberta.ca)
*
✉For correspondence; e-mail: RLStewart@ieee.org
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Abstract

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Given a rectangle containing uniformly distributed random points, how far are the points from the rectangle’s centre? In this paper we provide closed-form expressions for the cumulative distribution function and probability density function that characterise the distance. An expression for the average distance to the centre of the rectangle is also provided.

Keywords

rectangledistribution of distancesprobability density functioncumulative distribution functionmean distancerectangle pickingrobotic computer vision

MSC classification

Secondary: 60D05: Geometric probability and stochastic geometry
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 87 , Issue 1 , February 2013 , pp. 115 - 119
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

Footnotes

The authors would like to gratefully acknowledge partial funding of this work by NSERC. Robert Stewart would additionally like to acknowledge the support of a Postdoctoral Fellowship from the University of Alberta while he was on leave without pay from an Australian research organisation.

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