These routines compute the transverse Mercator projection by means of a
novel Fourier-based technique, which is much more efficient than
conventional methods based on the evaluation of power series if you want
to project a large number of points (say 32 or more along a meridian).

The method is described in a paper, "Efficient computation of the
transverse Mercator projection", which is currently being refereed.  The
paper is not available on-line.

I haven't tried to optimize this code to the fullest extent.
In particular, in places, trivial multiplications are avoided by a run-
time test to see if either operand is 0 or 1.  This is not cheating
(although it looks like it), because in each case the fact that the
multiplication is trivial is known "a priori", independently of the
data, and a "proper" implementation would make the appropriate
optimizations.	So the operation counts reported by the program, and
documented in the paper, really are realistic and accurate.

Honestly!

A.J. Fisher