Transverse Mercator Projection
This page is a web resource for the paper
Charles F. F. Karney,
The implementation of the series and exact algorithms are
available as part of GeographicLib which is licensed under the
see LICENSE.txt for the terms.
Transverse Mercator with an accuracy of a few nanometers,
J. Geodesy 85(8), 475–485 (Aug. 2011);
A good way to visualize the transverse Mercator projection
over the entire global is using
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.
open the "tm-grid" folder in Google Earth and check on the
"spherical-transverse-mercator" 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 data 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):
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 $15).