[Proj] Comments of tmerc, etmerc and ftmerc errors

Gerald I. Evenden geraldi.evenden at gmail.com
Thu Jun 12 12:17:03 EDT 2008

Two testing grids were made on tmerc, etmerc and ftmerc: in a geographic range 
of 0 to 6 degrees longitude by 0 to 84 degrees latitude and 0 to 500km 
Easting to 9,700km Northing.  The most apparent problem is that for 
reasonable demonstration the results should be presented as contour maps of 
the errors but inclusion of same is not possible in this email list.

A simple summary can be made: in the lat-lon tests tmerc maintained an 
accuracy of <0.7mm (as would be expected occurred at the equator) and 
comparison of etmerc and ftmerc was always less than 1micron.  In the 
Easting/Northing test, tmerc failed dismally at 21 meters at about 58degrees 
longitude/84.78 degree latitude.  Again, ftmerc and etmerc maintained 
agreement to within 1micron.

I believe it is quite safe to say that tmerc remains the projection of choice 
for UTM applications: adequate accuracy performance and best computational 
speed. Note that the lat/lon test was for 12 degree zones and thus tmerc is 
would appear suitable for what I understand of the 10 degree zones used for 
some Canadian province grids.

As for extended range, I will probably check the agreement of etmerc and 
ftmerc over extended range but this is of lesser priority.  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.  Usage of conformal maps for 
global mapping is very questionable because of the distortion.  Normal 
Mercator persists only because of its usefulness in rhumbline navigation 
which is probably fading due to GPS.  Lastly, equal-area mapping is far 
preferable for thematic mapping as it at least give a better perspective of 
the area extent of regions that is, in most cases, more important that an 
often poor preservation of regional shape.
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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