Re: finding the area of highest concentration
From: James Waldby (j-waldby_at_pat7.com)
Date: 09/27/04
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Date: Mon, 27 Sep 2004 16:27:08 -0500
Joe wrote:
> Hi there. I am hoping that somebody may be able to offer me some
> advice here. Basically I have a series of rectangles in a Cartesian
> plane and I would like to find the area of highest density (also a
> rectangle). I know that so far this query is a little vague as
> different tolerance values could be specified. At the moment I am
> approaching this task at the most simplistic level. What I am doing is
> calculating the centre point of each rectangle in the plane and then
> finding out which of the other rectangles in the plane contain these
> points. The points contained in the highest number of frames may form
> the boundary of the area of highest concentration or simply lie inside
> it depending on their position in the plane. What I would like is for
> someone to offer me some sound advice on maybe a better method of
> achieving my goal or some proper mathematical way of finding the area
> of greatest density. Thsnks a lot, Joe
How is density defined? I haven't heard of the problem you
mention so I don't know if there are standard definitions and
conventions for it. If so, you might provide a reference; if
not, you will need to properly define density before thinking
about algorithms.
Also, perhaps you could tell us the answers to some simple cases:
For example, let U = {p, q} where p and q are axis-aligned unit
squares centered at (-1,0) and (1,0) respectively. What is
your answer for case U ?
For another example, let V = {p, q, s, t} where s, t are unit
squares tilted 45° and centered at (-1, -1/2) and (1, 1/2)
respectively. What is your answer for V ? (If you don't want to
consider any rectangles that aren't axis-aligned, instead consider
W = {p, q, s', t'} with s', t' centered like s, t, but not tilted.)
-jiw
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