From: dmark@acsu.buffalo.edu (David Mark)
Newsgroups: comp.infosystems.gis
Subject: Re: Confused about digital scales
Date: 14 Oct 92 10:53:55 GMT
Organization: UB

In article <19921013.174719.763@almaden.ibm.com> isw@vnet.ibm.com (Ian S Worthington) writes:
>
>Many thanks to all those who are responding to my novice questions here and
>direct to me. May I try and example to help clarify the matter?
>
>If I had a database which had a stated accuracy of, say, 25m, I would
>know that, if I reproduced a map on a monitor, then I should not allow
>the user to zoom in to a greater level of detail than 1 pixel = 25m.

I don't see that the pixel is very relavent.  If your device is now 300 pixels
per inch, and next year you get one that is 3000 pixels per inch, it does not
make sense to me that you would require users to make their maps 10 times 
smaller in their appearance on the screen.

>Similarly, if I plotted, or printed, from this database, the maximum
>size I should allow would be <the minumum reproducable physical
>distance> = 25m.  I think this is correct, yes?
>
>So, if instead of this I use a database with a given scale of 1:50
>000, how do I determine how 'close' to let a user zoom in?  Until the
>'virtual' screen/page is 50 000 pixels/points, maximum?

What I take it to mean is that if the source map were well-designed for 
1:50,000, then you should not allow the graphic on the screen to be
(much) larger than 1:50,000, or 1cm on the screen represents 500 m on the
ground.

>So, on the basis, the accuracy of the DCW with quoted scale of
>1:1 000 000, is approx 40m, from:
>
>   Circ. of earth at equator ?= 360 x 60       = 21 600 mautical miles
>                             ?= 1.1 x 21 600   = 23 760 statute miles (I think?)
>                             ?= 8 / 5 * 23 760 = 38 016 kilometers
>
>   then:
>             38 016 km / 10
>
>Is this anything like correct?

Not really.  If the 1:1,000,000 ONC maps that the DCW was derived from
met the US Geological Survey's map accuracy standards, then 90% of points
would be withing 1/50 inch (0.5 mm) of their correct positions on the paper
map.  This corresponds to about 500 meters on the ground.
>
>If so, isn't it of more use to quote the minumum *accuracy* of the
>data to start with?

What you are missing is that, when we are talking about printed maps, there 
is more to mapping than just positional accuracy.  Maps involve generalization,
simplification, selection, symbolization.  Detail that may be known to the
map-maker is deliberately left out (reducing positional accuracy, byt the way)
in order to achieve visual clarity in the graphic product.  You cannot make a
useable 1:1,000,000 map just by taking a 20 by 20 set of 1:50,000
scale maps, pasting them into a mosaic, and reducing them by a factor of 20.
They would be unreadable.  But if you thickened all the lines by a factor
or 20, then they would overlap, self-intersect, etc.

If maps have been prepared according to the traditional standards of 
topographic mapping, then the scale is quite a good summary of the degree
of generalization that will have gone on.  There is no over-all positional
accuracy, or resolution, because contours may have been smoothed (generealized)
more than, say, coastlines, for cartoGRAPHIC reasons.

So, if like DCW, the data in a geographic database have come from a single 
series of maps at a particular scale, then the scale of that series is 
probably the best available summary of the 'nature' of the dataset.

Now, in a sense, these constraints do not apply in digital databases, and the
way to summarize a database compiled in the field using GPS and
surveying techniques would be difficult.  But the scale constraints on
generalization and design apply whenever the data are plotted graphically
on a CRT or on paper.

David Mark
dmark@sun.acsu.buffalo.edu
Newsgroups: comp.infosystems.gis