Transverse Mercator Projection
This page is a web resource for the paper
Charles F. F. Karney,
Transverse Mercator with an accuracy of a few nanometers,
J. Geodesy 85(8), 475–485 (Aug. 2011);
preprint arXiv:1002.1417
(pdf);
addenda.
The implementation of the series and exact algorithms are
available as part of GeographicLib which is licensed under the
MIT/X11 License;
see LICENSE.txt for the terms.
Additional material:

A good way to visualize the transverse Mercator projection
over the entire global is using
tmgrid.kmz,
which is a Google Earth KML file showing the transverse
Mercator grid (in red) for the WGS84 ellipsoid with grid
spacing 1000 km in the x and y directions. The
scale, k = 0.9998035, has been adjusted so that the
distance from the equator to a pole is 10000 km.
If you
open the "tmgrid" folder in Google Earth and check on the
"sphericaltransversemercator" subfolder, you will also see
the corresponding spherical transverse Mercator grid (in
yellow) conformally mapped to the WGS84 ellipsoid. (This
doesn't have a constant scale on the central meridian.)

Test set for the transverse Mercator projection:
Use only the entries with latitude ≥ 0 for testing an
algorithm with the standard convention for the branch cut.

Maxima implementation of Lee's exact method (arbitrary precision):
tm.mac
and ellint.mac. There is brief
documentation at the top of tm.mac.

The paper gives Krüger's series accurate to 8th order;

Krüger's 1912 paper.

Relevant section of Lee's 1976 paper (price $13).
Charles Karney
<charles@karney.com>
(20141130)
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