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| Subject: | RE: [gislist] spatial question - put your thinking caps on |
| Date: |
11/26/2003 01:55:01 PM |
| From: |
David Melton |
|
|
Rick et al.,
Ooh, these are good questions! To answer your first question, let's =
assume
that your points fall along a fixed network, and that you have to stay =
on
the network to visit each point, rather like customers on a paper route. =
If
you're already traveling most of the streets in a neighborhood to =
deliver
papers, then doubling the number of customers won't increase the =
distance
you have to travel, unless you add a customer that is on a new street.
To answer your second question, the average distance between points and =
the
density are not a linear relation. Starting with an n by n grid, you =
have
to add 3n^2 - 4n + 1 points in order to halve the distance between =
points.
This can be lamely illustrated in ASCII below:
* + * + *
+ + + + +
* + * + *
+ + + + +
* + * + *
Starting with the 3x3 grid of asterisks, you would have to add 16 =
points,
represented by plus signs, in order to cut the distance between points =
in
half. If there were n^2 points in the original grid, there will be =
(2n-1)^2
points in the second grid.
Another way to look at the relationship between density and the distance
between points is to consider a 3 by 3 grid containing 9 points. =
Keeping
the number of points constant, in order to halve the distance between
points, you have to shrink the grid so it takes up 1/4 the original =
space.
Again, this can be lamely illustrated below:
* * *=20
* * *
* * *
halving the distance between the points results in a grid that takes up =
1/4
the original space:
* * *
* * *
* * *
I realize these are extreme generalizations of your questions, but =
hopefully
they will get you started toward an answer for your boss.
Regards,
David Melton
Digital Mapping Solutions LLC
-----Original Message-----
From: gislist-bounces@lists.geocomm.com
[mailto:gislist-bounces@lists.geocomm.com] On Behalf Of RICK GRAY
Sent: Wednesday, November 26, 2003 1:06 PM
To: gislist@lists.geocomm.com
Subject: [gislist] spatial question - put your thinking caps on
Not directly a GIS question, but as a spatially-enabled group, I'm
hoping someone here can offer some pointers.=20
I have a set of points with a known density. If I double the density,
will I increase the distance incurred to travel to all the points? What
will be the mathematical relationship between average distance between
points (or the sum thereof) and their density? =20
Of course I realize there are a lot of factors, not least of which will
be the pattern of distribution and the pattern of road networks, but can
I generalize in some fashion?=20
My boss has thrown this at me as he wishes to quote on a maintenance
contract and wants to know: if the # of units in a given area is
doubled, how will it affect our costs.
Thanks in advance
Rick
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