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

Noel Zinn ndzinn at comcast.net
Sat Jun 14 11:43:14 EDT 2008

Bravo, Gerald!  

Your mention of geocentric x-y-z is consistent with a minority view
(growing, I hope) within the oil exploration IT community that all of
cartography (not just conformal, and including all the distortions that
cartography is heir to) can be done away with.  Our newest generation of
geophysical interpretation workstation applications works in 3 orthogonal,
linear coordinates without any hint of geodetic or cartographic awareness.
Why distort a 3D world into 2D horizontally (called a map projection, with a
third vertical dimension tacked on), when the 3D world can be represented
"in the box" in 3D in geocentric x-y-z (AKA Earth-Centered Earth-Fixed, or
ECEF)?  The view is that of Google Earth or ESRI's ArcGlobe, but one can
penetrate the Earth to any target depth.  Seems like a no-brainer.  When
will pigs fly?  Soon, I hope.  It makes sense.

Noel Zinn

PS - ECEF does present its own problems, but they're not geodetic or
cartographic problems about which computer whiz kids know little.  Give them
a coordinate system they understand (trigonometry in 3 dimensions) and
miracles will happen!

-----Original Message-----
From: proj-bounces at lists.maptools.org
[mailto:proj-bounces at lists.maptools.org] On Behalf Of Gerald I. Evenden
Sent: Saturday, June 14, 2008 10:09 AM
To: PROJ.4 and general Projections Discussions
Subject: Re: [Proj] Re: Comments of tmerc, etmerc and ftmerc errors

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
> 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
> 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
advised.  I feel it is fair to say most small scale map usage is in the
of thematic mapping and and in such usage I feel that the principal factor
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
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 

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
projection that properly displays the intent of the map and I can drop a
anywhere on the map and know that it covers the same number of square

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 

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
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

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