MI Flavors of Transverse Mercator

[Cliff Mugnier - University of New Orleans]

Fernando,

The GCTP.FOR is a Fortran77 source file (free from the "USGS.gov" websites) for
all of the map projections used by the U.S. Geological Survey.  There are two
data files associated with the source code that are included also.  The math was
documented by John P. Snyder (now deceased) in "Map Projections Used by the U.S.
Geological Survey" Bulletin 1532, and later revised as "Map Projections - A
Working Manual" Bulletin 1535.  Bulletin 1535 is better because it has more
projections and Mr. Snyder referenced me (ha, ha)!   :-)

Anyway, Dr. Atef Elassal (now retired), then translated 1532 into Fortran for
the USGS.  That is GCTP - the General Cartographic Transformation Package which
is specifically for cartographic applications within the United States.  That's
what the data files are for.  GCTP is absolutely perfect for what it was
intended for - INSIDE THE UNITED STATES OF AMERICA ONLY ! ! ! ! ! 

Many, many commercial software packages worldwide use this as the basic
foundation for their coordinate transformation engine.  I give it away to my
students as an example of "how not to do it."  This is essentially useless for
geodetic applications outside of the United States.  It can oftentimes be used
for cartographic applications outside of the U.S. IF AND ONLY IF the
computational accuracy (and precision) is not needed for mapping at scales
larger than 1:24,000!!!!!!!

If you are going to use this for a NON-geodetic application, this will do just
fine.  If you are doing geodesy, do not touch this code!

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The ellipsoidal case of the Transverse Mercator was cooked up by Heinrich
Lambert in the middle 1700's.  It was a mathematical curiousity that was useless
for practical applications until the City of Hannover asked Professor Carl
Freiderich Gauss to do a geodetic survey of the city in preparation for a new
set of accurate tax maps.  

There are two things you cannot avoid in life; those are death and taxes.  Most
all geodetic research has been funded (since the late 1700's) for either tax
mapping purposes or military purposes looking for better and more efficient ways
of killing people ...

Anyway, Gauss worked up an expansion of Lambert's formulae that his Ph.D.
students could follow in doing the grunt work of adjusting the Hannover
Triangulation Net on the Gauss-Conformal Transverse Mercator.  Years later, a
Prussian Artillery Office named Schreiber used a simplified form of the
Gauss-Conformal Transverse Mercator that was a specific truncation called the
Gauss-Schreiber Transverse Mercator.  Another Prussian Artillery Officer named
Krüger came up with a more elaborate expansion of the infinite series.  Yup, it
is called the Gauss-Krüger Transverse Mercator.  In the 1920's or 1930's an
Italian Professor in Italy came up with a local version for the Instituto
Geografico Militare, and his name was Boaga.  Yup, the Italians use the
Gauss-Boaga Transverse Mercator.  And so on and so forth for ALL the ellipsoidal
projections used for Grids on topographic maps.

When looking at geodetic accuracy and computational precision at the
sub-millimeter level TO THE MULTI-METER LEVEL for coordinates many degrees east
or west of the central meridian, the specific truncation of a Transverse
Mercator makes a big difference. Doing foreign work for bazillion-dollar
exploration, drilling, and production for oil wells in specific countries?  Pay
attention to your math. If you are doing UTM or DHG (Deutches Herres Gitter)
within a plus or minus 3 degree longitude distance from the Central Meridian, it
will do fine.

Diddling with some X,Y coordinates for a Ph. D. dissertation?  Unless your Major
Professor is a geodesist or mathematical cartographer, they won't even know the
difference.

Cliff

-- 
Clifford J. Mugnier ([EMAIL PROTECTED])
The Topographic Engineering Laboratory
Department of Civil and Environmental Engineering
UNIVERSITY OF NEW ORLEANS
New Orleans, Louisiana  70148

Voice and Facsimile: (504) 280-7095
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Fernando wrote:
> 
> Hello Cliff
> 
> I am doctorate student that needs to program a convert from Gauss
> Krüger to lat. long and back. The ideal solution would be to get a
> Fortran code for this, but maybe that is too much luck, so I would be
> happy with any hint you can give me (if I do not have to buy any
> software or module, even better).
> 
> I have already spent a lot of time looking for it in Internet and I have
> found nothing, except your name in 'users.netonecom.net' (1998).
> 
> And I have another question that confuses me (I am a beginner on this):
> Is Gauss-Krüger the same Transverse Mercator, or there is an important
> difference?
> 
> Thanks in advance for any help,
> 
> Fernando
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