Re: how to calculate the expected distance from a point to the center in square grid?

From: David W. Cantrell (DWCantrell_at_sigmaxi.org)
Date: 10/08/04 

Date: 08 Oct 2004 04:43:22 GMT

"Leonardo B. Oliveira" <leob@dcc.ufmg.br> wrote:

> The expected distance between a random point
> (i.e., a point picked at random) in a circle of
> radius R and the center of this circle
> is R sqrt(2)/2 - as shown in "Estimating Hop=20
> Counts in Position Based Routing Schemes for Ad Hoc"

I'm not familiar with that article.
And I must wonder if you're presenting their result accurately. I seems to
me that what you have described as "expected distance" should be merely
the average distance from the center of the circle to points within it,
and that distance is 2/3*R, not sqrt(2)/2*R.

> But and what about the expected distance from random
> point to the center of a square grid, say n x n?

To make this case easily comparable to that of the circle, let's say
instead that we're dealing with a square of side length 2*R. The average
distance from the center of the square to points within it is then

 (sqrt(2) + log(1 + sqrt(2)))*R .

David Cantrell

Relevant Pages

  • Horizon Problem Resolution (2/28/09)
    ... Inflation theory has been offered as a way to overcome this `Horizon Problem'. ... The inner circle of radius $r$ represents space at an earlier time. ... The cosmological redshift, $z$, is ... \section{Velocity Redshift and Distance Redshift Relations} ...
    (sci.physics.particle)
  • Horizon Problem Resolution (2/28/09)
    ... Inflation theory has been offered as a way to overcome this `Horizon Problem'. ... The inner circle of radius $r$ represents space at an earlier time. ... The cosmological redshift, $z$, is ... \section{Velocity Redshift and Distance Redshift Relations} ...
    (sci.physics)
  • Horizon Problem Resolution (2/28/09)
    ... Inflation theory has been offered as a way to overcome this `Horizon Problem'. ... The inner circle of radius $r$ represents space at an earlier time. ... The cosmological redshift, $z$, is ... \section{Velocity Redshift and Distance Redshift Relations} ...
    (sci.astro)
  • Re: Circle - Square Collision Detection
    ... where the circle and square are far enough apart that they can't ... do a signed point to line distance calculation ... If the signed distance is less for ANY edge of the square, ...
    (comp.games.development.programming.misc)
  • Re: A geometrical problem concerning distances
    ... that the distance from P to one of the two other corners is equal to 40. ... What is the length of the size of the square? ... that the circle of radius 4 is at the origin, ... We find by this check that only s_1 is a valid solution. ...
    (sci.math)