[Proj] Extended range TM usage

Gerald I. Evenden geraldi.evenden at gmail.com
Sun Aug 24 22:08:03 EDT 2008

I am finishing up the revised transverse Mercator section of libproj4's manual 
which includes three additional versions of the projection that give an 
extended longitude range for the projection.  These version persist in being 
singular at the equator and 90 degrees from the central meridian.  Hopefully, 
I may soon obtain a copy of Lee's work and include the Ultimate version.

The old Taylor series version (tmerc) of TM is shown to be quite adequate for 
cadestral applications as demonstrated by comparisons with the expanded 
versions,  That is, it has sub-millimeter accuracy within all longitude zones 
of standard applications that I am aware of.

At the current time I consider the work on the extended version academic and 
of little practical application for the following reason: scale error of TM 
beyond an easting of about 400km (approximately 3.5 degrees longitude at the 
equator) would appear too large to make the projection useful in any 
application other than general mapping. If general mapping is the application 
then using the spherical form of tmerc should be adequate---especially for 
small scale maps.  The problem of the singularity of the projection at 
(+-90,0) is not a problem because the distortion is so severe at the right 
and left edges the sides can be clipped.

My question is can anyone supply a rational reason for the practical use of an 
elliptical TM projection with extended longitude range.  The explanation 
should discuss how the projected coordinates are used and how the error 
factor is handled in application of the coordinates (like determining 
distance between points, azimuth, etc.).  Of course, how precise do you 
expect such measurements to be?

I would like to include some practical applications for using the added 


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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