[Proj] Transverse Mercator algorithm

[Gerald I. Evenden]

On Tuesday 27 May 2008 11:52 am, Frank Warmerdam wrote:
> Oscar van Vlijmen wrote:
> > In my opinion, there are 2 possibilities:
> >
> > * High accuracy.
> > * Speed.
>
> Folks,
>
> To state the obvious, computers are pretty fast now, so for many purposes
> a TM variant that is quite a bit slower would be acceptable.
>
> I would like to see a TM version that is very reversable well outside the
> typical six degree swath around the central meridian.
>
> Mostly I wish I could have a highly reversable TM variant that was exactly
> the same as the existing TM approximation in at least one direction.  It is
> the failure to reverse that is a nightmare for me.

A minor nit-pick: "inverse" is a better term than "reverse."

arcsine is the inverse of sine.

Another minor aside: an earlier version of proj used with the mapgen program 
used a Tchebyshev(sp) approximations to speed up the projections for larger 
scale map regions (lesser lam-phi extents).  This also alowed the code in the 
mapping program to only deal with bivariate polynomials for all projections 
and not have to carry around the projection library.

-- 
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