Transverse Mercator Projection

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.

• GeographicLib home page
• GeographicLib documentation
  • The C++ class TransverseMercator, which implements the Krüger series method.
  • The C++ class TransverseMercatorExact, which implements the Lee's exact method.
  • The utility TransverseMercatorProj, for testing the implementations.
  • The utility GeoConvert, for UTM and MGRS conversions and an online coordinate converter.
• Download GeographicLib

Additional material:

• A good way to visualize the transverse Mercator projection over the entire global is using tm-grid.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 "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): 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 series to 10th order;
  • Krüger's series to 30th order, tmseries30.html;
  • Maxima code to generate Krüger's series to arbitrary order, tmseries.mac (there is brief documentation at the top of the file);
  • download maxima.
• Krüger's 1912 paper.
• Relevant section of Lee's 1976 paper; borrow from archive.org.