# [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..."
>
>
> 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
pi/2.

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
copy.

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
```