[Proj] Transverse Mercator algorithm

Charles Karney ckarney at sarnoff.com
Thu Sep 4 08:16:45 EDT 2008

Mikael Rittri wrote:
> Charles Karney wrote:
>> The Finnish algorithm is related.  The series relating [xi,eta] and
>> [xi',eta'] are just expansions (in eccentricity) of the
>> transformation between two of the TM projections described on p. 92
>> of Lee's 1976 monograph (namely what he calls the spheroidal
>> projection [xi',eta'] and the Gauss-Krueger projection [xi,eta]).
> Am I right in thinking that the spheroidal projection [xi', eta'] is
> the same as Gauss-Schreiber?  Except that xi' and eta' are based on an
> ellipsoid whose radius is 1. (Sorry, I am not quite sure what I mean
> by ellipsoid radius in the previous sentence.)

Yes.  However, there seems to be a fair amount of confusion on the
naming of the various transverse Mercator projections...  To quote from
p. 101 of

      L. P. Lee,
      Conformal Projections Based on Elliptic Functions,
      (B. V. Gutsell, Toronto, 1976), 128pp.,
      ISBN: 0919870163.


  The projection given by (56.1) [the xi',eta' projection] was due to
  Gauss 1843, who derived it by first projecting the spheroid
  conformally upon a sphere so that all the meridians correspond, and
  then making a transverse Mercator projection of this sphere. It was
  described by Schreiber 1897, and is sometimes known as Schreiber's
  double projection. It was also described by Krueger 1914. The name
  Gauss-Laborde is used to describe it in Prance. It was derived in a
  more general form by Hotine 1947.

  The names, Gauss-Schreiber and Gauss-Krueger, as used by Lee 1962 do
  not accord with European usage.

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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