Transverse Mercator formulae

I am working on implementing the formulae for Transverse Mercator in a
Java Map Projection Package. I have implemented the formulae given on
pp 60- 64 of Snyder (1987) , Map Projections - A Working Manual.
However, these are not accurate beyond 5-10 degrees from the central
meridian. I have also found the paper referenced by Snyder as "Army,
1962" that gives more terms for the equations; I haven't tried it yet
but it only claims accuracy to 24 degrees.

However, both these document only Taylor expansions of the original
unclosed equations, and do not give the "open" forms of the equations,
stating that they are of little practical use because they converge
too slowly.

These days, I wonder if this is true! Processing power is far greater
than it was in 1987, and I would like to have a go at implementing an
iterative solution using the basic "open" form of the equations, in
the same manner as I usually do for other projections. Here we hit a
snag, though - I don't have a reference for them; everyone seems just
to give series based solutions. Can someone point me in the right
direction?

It seems to me that as long as I have a form that converges, it is
unlikely that it would be so slow as to be unuseable in the
environment I am working in, and it would be far more accurate.

Thanks

Paul Cooper
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Maybe this is helpful:
http://www.dwaf.gov.za/IWQS/gauss/gauss.html

On Tue, 26 Feb 2008 19:10:30 -0800 (PST), user923005


Thanks, I'd already found that one. It still uses Taylor expansions,
but I haven't looked at it in detail. It is a shame it is published in
HTML so it is difficult to print it all out!

Paul