[Proj] Complex Transverse Mercator

Gerald I. Evenden gerald.evenden at verizon.net
Wed Jun 28 12:45:54 EDT 2006

Sorry that I did not reply earlier.
On Tuesday 27 June 2006 1:34 pm, Oscar van Vlijmen wrote:
> From: Strebe-aol.com:
> You might avail yourself of a copy of L.P. Lee's monograph, "Conformal
> Projections Based on Elliptic Functions", Cartographica, Monograph Number
> 16, 1976. Quoting verbatim from p. 97:
> "The positive y-axis represents part of the equator, extending from lambda
> = 0 to lambda = (pi/2)*(1-k)... At this point the equator changes smoothly
> from a straight line to a curve... The projection of the entire spheroid is
> shown in Fig. 46, again using the eccentricity of the International
> (Hayford) Spheroid. It can be seen that the entire spheroid is represented
> withing the finite area without singular points..."
> Reply:
> Thanks for this explanation!
> The numbers show it too:
> International ellipsoid:
> 90*(1-eccentricity) = 82.62073 decimal deg

I strongly do not believe any of these new extended TMs should be use for UTM 
as the "standard UTM" is defined as the taylor expansion---warts and all.  
Anyone who has abused the limits of UTM will have trouble when using new 
versions.  Secondly, UTM is bound by "law" to the limits of +-3.5 degrees so 
these extensions are immaterial.

> Tranverse Mercator:
> lat0=0; lon0=0; x0=5e5; y0=0; k0=0.9996;
> // International ellipsoid
> lat=0; lon=82.50;  x,y = 18712722.276, 0 meters
> lat=0; lon=82.60;  x,y = 18840409.942, 0
> lat=0; lon=82.61;  x,y = 18853673.034, 0
> lat=0; lon=82.62;  x,y = 18867090.964, 0
> lat=0; lon=82.621; x,y = 18868446.553, 0.2947
> lat=0; lon=82.63;  x,y = 18880722.285, 107.602
> lat=0; lon=82.64;  x,y = 18894438.954, 366.186
> lat=0; lon=82.65;  x,y = 18908216.295, 738.078
> lat=0; lon=82.70;  x,y = 18977788.411, 3947.057
> lat=0; lon=82.80;  x,y = 19119409.657, 15745.905

As per  my comments three years ago, none of this make any intuitive sense.  
This probably explains why the German web page deviates as one approaches 

BTW, how do these numbers stack up with the German web page.

I seem to recall the Lee article and must double check that I might have it 
and forgotten about it.  If I do not have it, it is a pain to try and get a 

The forward is functioning in libproj4 but I have not done any polishing other 
than trimming Dozier's code.  I'll check out the inverse (which is coded) 
this PM and then start looking at the details.
Jerry and the low-riders: Daisy Mae and Joshua
"Cogito cogito ergo cogito sum"
   Ambrose Bierce, The Devil's Dictionary

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