A note concerning the distances of uniformly distributed points from the centre of a rectangle

Robert Logan Stewart, Hong Zhang

Abstract


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.

DOI: 10.1017/S0004972712000421

Keywords


Rectangle, Distribution of Distances, Probability Density Function, Cumulative Distribution Function, Mean Distance, Rectangle Picking, Robotic Computer Vision



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Bulletin of the Aust. Math. Soc., copyright Australian Mathematical Publishing Association Inc.