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<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01//EN"
"http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<title>
Transverse Mercator Projection
</title>
<meta name="description" content="Transverse Mercator Projection" />
<meta name="keywords"
content="transverse Mercator projection,
Gauss-Krueger projection,
universal transverse Mercator,
UTM,
conformal projections,
WGS84 ellipsoid,
latitude and longitude" />
<meta name="author" content="Charles F. F. Karney" />
</head>
<body topmargin=10 leftmargin=10>
<h3>Transverse Mercator Projection</h3>
<p>
This page is a web resource for the paper
<blockquote>
Charles F. F. Karney,<br>
<a href="https://dx.doi.org/10.1007/s00190-011-0445-3">
<i>Transverse Mercator with an accuracy of a few nanometers</i></a>,<br>
J. Geodesy <b>85</b>(8), 475–485 (Aug. 2011);<br>
preprint <a href="http://arxiv.org/abs/1002.1417">arXiv:1002.1417</a>
(<a href="http://arxiv.org/pdf/1002.1417">pdf</a>);<br>
<a href="tm-addenda.html"><b>addenda</b></a>.
</blockquote>
The implementation of the series and exact algorithms are
available as part of GeographicLib which is licensed under the
<a href="http://www.opensource.org/licenses/MIT">MIT/X11 License</a>;
see <a href="html/LICENSE.txt">LICENSE.txt</a> for the terms.
</p>
<ul>
<li>
<a href="index.html">GeographicLib home page</a>
<li>
<a href="html">GeographicLib documentation</a>
<ul>
<li>
The C++ class
<a href="html/classGeographicLib_1_1TransverseMercator.html">
TransverseMercator</a>, which implements the Krüger
series method.
<li>
The C++ class
<a href="html/classGeographicLib_1_1TransverseMercatorExact.html">
TransverseMercatorExact</a>, which implements the Lee's exact
method.
<li>
The utility
<a href="html/TransverseMercatorProj.1.html">
TransverseMercatorProj</a>, for testing the implementations.
<li>
The utility
<a href="html/GeoConvert.1.html">
GeoConvert</a>, for UTM and MGRS conversions and an
<a href="cgi-bin/GeoConvert">
online coordinate converter</a>.
</ul>
<li>
<a href="https://sourceforge.net/projects/geographiclib/files/distrib">
Download GeographicLib</a>
</ul>
<p>
Additional material:
</p>
<ul>
<li>
A good way to visualize the transverse Mercator projection
over the entire global is using
<a href="tm-grid.kmz"
type="application/vnd.google-earth.kmz"> tm-grid.kmz</a>,
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 <i>x</i> and <i>y</i> directions. The
scale, <i>k</i> = 0.9998035, has been adjusted so that the
distance from the equator to a pole is 10000 km.<br> 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.)
<li>
Test set for the transverse Mercator projection:
<ul>
<li>
the
<a href="https://sourceforge.net/projects/geographiclib/files/testdata/TMcoords.dat.gz/download">
data set</a>;
<li>
<a href="html/transversemercator.html#testmerc">
documentation</a> for the data set.
</ul>
Use only the entries with latitude ≥ 0 for testing an
algorithm with the standard convention for the branch cut.
<li>
Maxima implementation of Lee's exact method (arbitrary precision):
<a href="html/tm.mac">tm.mac</a>
and <a href="html/ellint.mac">ellint.mac</a>. There is brief
documentation at the top of tm.mac.
<li>
The paper gives Krüger's series accurate to 8th order;
<ul>
<li>
<a href="html/transversemercator.html#tmseries">
Krüger's series to 10th order</a>;
<li>
Krüger's series to 30th order,
<a href="html/tmseries30.html">tmseries30.html</a>;
<li>
Maxima code to generate Krüger's series to arbitrary order,
<a href="html/tmseries.mac">tmseries.mac</a> (there is brief
documentation at the top of the file);
<li>
<a href="http://maxima.sourceforge.net/">download maxima</a>.
</ul>
<li>
<a href="https://dx.doi.org/10.2312/GFZ.b103-krueger28">
Krüger's 1912 paper</a>.
<li>
<a href="https://dx.doi.org/10.3138/X687-1574-4325-WM62">
Relevant section of Lee's 1976 paper</a> (price $13).
</ul>
<hr>
<address>Charles Karney
<a href="mailto:[email protected]"><[email protected]></a>
(2014-11-30)</address>
<br>
<a href="http://geographiclib.sourceforge.net">
GeographicLib home
</a>
</body>
</html>