On Wed, 23 Feb 2005 12:24:21 -0000, "John Rowland"
wrote:

"Larry Lard" wrote in message
oups.com...


Anyway, I'm not really sure this branch of this thread (?) has anything
useful to say about the original problem, as raised by Michael Dolbear:
"I think it can't be done on a flat map without rearranging the order
of stations on each line."

His statement is so clearly wrong it's hard to argue with it until someone
explains why they think it's right. Every public point in the 2D space has a
scalar quantity associated with it, namely journey time from point X.
Mathematically this is identical to the contour maps, where every point
which is not inside a building has a scalar quantity associated with it,
namely height above sea level.

That's broadly correct, but there is a difference in that whereas
height is a continuous quantity which has a value for *every*
location, journey time from X only has a value at discrete locations,
namely those where there are stations. So if you want to construct a
contour map (or a carpet plot) on a map of (say) England then you need
to interpolate between the values using a straight line or a
mathematical function that does it more smoothly.

Here's an example: if it takes 40 minutes to West Drayton and 25
minutes to Slough (I'm guessing these times), then where does the "30
minute contour" run? The answer is it passes somewhere between the two
stations. The exact position depends on what type of interpolation you
are using.

Note that you don't only have to interpolate between adjacent stations
on the same line - you need to interpolate between adjacent stations
irrespective of whether there is a railway between them, to allow you
to work out, say, where the 30 min contour line passes between Slough
and Gerrard's Cross.

There is software around that will do all this and take a set of
(X.Y) point and plot the Z value using contours. There are three steps
we need to take:

* obtain the Grid Reference (X,Y) of every station in (say) the
south-east. Does this data already exist?
* look up the fastest peak journey time (Z) from somewhere to each
station
* plot the resulting data as a contour plot

PaulO