[Proj] C++ code for exact Transverse Mercator Projection

Charles Karney ckarney at sarnoff.com
Wed Sep 17 15:12:31 EDT 2008

> I think a clarification is needed and, indeed, part of the problem is
> mine.  When I speak of the Krueger solution I am referring to the
> Taylor series as expressed by PD Thomas "Conformal Projections in
> Geodesy and Cartography (1952), p. 2-3, which form the basis for
> standard TM as used in UTM and other grid system applications and is
> what is implemented in libproj4.  In some cases, the series is
> truncated even further.  I have not seen the Krueger paper but assumed
> it was somewhat similar to Thomas and represented the same basic
> solution.  Perhaps we/i should refer to tmerc as the Thomas TM--- the
> 't' in tmerc is for Thomas.

Krueger presents a Taylor series approximation accurate to e^8.  This is
what you've got with etmerc, ftmerc, and ktmerc (except that one of them
has the series extended to e^10).

Unfortunately, I don't have Thomas's book.  But from the expressions in
tmerc (and from the behavior of the errors), it looks like an ADDITIONAL
Taylor series expansion has been done in longitude.  This would
eliminate all the sinh's and cosh's of the Krueger method.

So, no, Krueger and Thomas are not the same.

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

More information about the Proj mailing list