[Proj] Transverse Mercator algorithm

[Gerald I. Evenden]

On Thursday 04 September 2008 3:58:12 pm Charles Karney wrote:
> Charles Karney wrote:
> > It'll take a day or so to make my macsyma code for the exact transverse
> > Mercator transformation presentable.

WARNING: anyone doing test with this script needs to know that the scale 
factor is also set to 0.9996.  The ellipsoid was reference OK but not knowing 
the scale factor had be set had me running around in circles for a minute.

> Start maxima and enter
>
>     load("tm.mac")$
>     xya:tm1(0b0,90b0)$
>     float(xya);
>     lla:ll1(xya[1],xya[2])$
>     float(lla);

I was comparing this to etmerc, ftmerc, ktmerc to see where they break down.  
Initially I could not find anywhere they agreed and was about to complaing 
when it struck me that k_0 may have been set.  Seems the vanilla 
initialization had been commented out and replaced.

In lproj parlance the setup is: +ellps=WGS84 +k_0=0.9996

-- 
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