[Proj] Re: Comments of tmerc, etmerc and ftmerc errors

[Gerald I. Evenden]

On Saturday 14 June 2008 12:37 am, strebe wrote:
> On Jun 13, 2008, at 2:56:35 PM, "Gerald I. Evenden"
> <geraldi.evenden at gmail.com> wrote: My sentense had nothing to do with area
> and by Cartesian usage I was denoting measuring distances, azumuths, etc.
> from the Cartesian data and it certainly seems that scale error greatly
> affects these measurements.
> Yes. Scale error greatly affects those measurements... but you're not going
> to get any better results with equal-area maps for those measurements than
> you will from conformal. That is because the "scale error" is just as
> pronounced in equal-area maps as it is in conformal maps. Hence...
>
> "Extended geographic range usage of any conformal projection is a
> contentious issue as any resultant grid system has sufficiently large scale
> errors as to make the Cartesian usage of the grid very questionable."
>
> ...does not follow. The only clearly improved measurement you'll get from
> equal-area maps is measurement of, well, area. You'll generally find
> approximations of azimuths to be much easier on conformal maps than
> equal-area. Distances are a mess on conformal or equal-area either one.

This is the place where we will apparently never agree.  I would never use 
small scale maps for distance/azimuth measurements and anyone who does is ill 
advised.  I feel it is fair to say most small scale map usage is in the realm 
of thematic mapping and and in such usage I feel that the principal factor of 
concern is the sense of extent of a feature and its *area* of scope.  A kind 
of "my area is bigger than yours" attitude.

The best example of worst case usage of a conformal map is the classic 
Mercator map of the world.  One of its few practical uses is to demonstrate 
the foible of measuring with this map and the rhumb line (loxodrome) and its 
relation to the prefered measurement of a great circle or geodesic. It is 
even rediculous to call it a map of the world when it can't even show the 
poles due to the ultimate distortion of a singularity.

Lastly, I can put a dime on an equal-area map and the area that the dime 
covers---in terms of real acreage on the ground---is the same anywhere on the 
map,  If I am looking at comparative areal extents of oil fields I have a 
reliable  method of comparison with the equal-area  map.  As for actual 
measurements I can use a planimeter on the map and get a direct error-free 
measurement.

If I were making a map of the areal extent of oil reserves in the Gulf of 
Mexico I would definitely use an equal area map.  This is the *only* class of 
projection that properly displays the intent of the map and I can drop a dime 
anywhere on the map and know that it covers the same number of square meters.

Lastly, I cannot think of a practical use of a conformal map of the Gulf 
because all practical problems of distance/azimuth determination are micro 
computer (or possibly shirt pocket calculator) functions with accuracy far 
exceeding any scale layed on a map---and I do not mean using a cartographic 
projection as an intermediate step unless it is to get data into the proper 
units.

In fact, lets abolish conformal mapping altogether after we make sure all 
coordinates of interest are stored as either geographic or geocentric x-y-z.
No more UTM, bastardized UTM, state/national plane coordinate system with wild 
a wooly projections.  Ahhh!  Utopia!  Unfortunately, when pigs fly.

> Regards,
> -- daan Strebe

-- 
The whole religious complexion of the modern world is due
to the absence from Jerusalem of a lunatic asylum.
-- Havelock Ellis (1859-1939)  British psychologist