[Proj] Transverse Mercator algorithm

Charles Karney ckarney at sarnoff.com
Thu Sep 4 15:58:12 EDT 2008

Charles Karney wrote:
> It'll take a day or so to make my macsyma code for the exact transverse
> Mercator transformation presentable.

OK, I've posted the maxima code for the arbitrary precision transversion
Mercator projection.  Go to


and download tm.mac and ellint.mac.  There's some meager documentation
in tm.mac.

Start maxima and enter


This converts the point 0N 90E to transverse Mercator (for WGS84) and
back to latitude and longitude.

float(xya) gives

    [2.595359284541359E+7, 9997964.943020998, 90.0, 18.40462279198669]

which is [easting(m), northing(m), convergence(deg), scale].

float(lla) gives [- 1.600614476517369E-82, 90.0] which approximates the
starting point.

The precision is 120 digits; so you should be typically getting results
which are good to at least half that many digits.

Charles Karney <ckarney at sarnoff.com>
Sarnoff Corporation, Princeton, NJ 08543-5300

URL: http://charles.karney.info
Tel: +1 609 734 2312
Fax: +1 609 734 2662

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