[Proj] Meaning of 7-parameter transformation rotations

[Jan Hartmann]

Frank Warmerdam wrote:
> On 11/30/05, Clifford J Mugnier <cjmce at lsu.edu> wrote:
> 
>>
>>
>>
>>Gentlemen:
>>
>>Note that the SENSE of the rotations have two common usages.  The American
>>Standard versus the European Standard differ!  To transform in the same
>>direction, the signs are OPPOSITE from one "standard" to another.
>>Generally speaking, a 7-parameter  transformation, whether it is a
>>Bursa-Wolfe or a Molodensky, MUST have a "test point" provided so that the
>>user knows which sense the rotations need for the desired transformation
>>direction.
>>
>>The Americans, Australians, and Luxemborgs use one SENSE, the Europeans use
>>the other.  In regard to the rest of the world, it depends on which
>>brand-name of GPS Geodetic Processing software was used to derive the
>>parameters from some collection of data points.  See my monthly column for
>>such important minutiae for country to country considerations.
>>
>>Be careful of 'dem signs!  :-)
> 
> 
> Cliff,
> 
> Your point is quite correct.  I believe that PROJ
> is using the European definition so that we can directly
> apply the numbers from EPSG.
> 

Yes, PROJ uses the "European" definition. Take as an example EPSG 
Coordinate Transformation 49, Amersfoort to ETRS89(1). The coefficients 
given here are "expressed in the standard NIMA righthanded rotation sign 
convention" (see Clifford Mugnier's column on Grids and Datums 
(http://www.asprs.org/resources/grids/ ,the Netherlands). For PROJ the 
rotation signs have to be reversed, so PROJ uses the left-handed sign 
convention common in Europe. Note also that PROJ uses arcseconds, EPSG 
microradians (in this case), so rotations have to be multiplied by 
0.206264806.

The equivalent parameters for EPSG and PROJ are in this case:
EPSG:
  565.04   49.91 465.84   1.9848  -1.7439  9.0587   4.0772
PROJ:
  565.04,  49.91 465.84  -0.4094   0.3597 -1.8685   4.0772


BTW: Dutch sources give both definitions:

http://www.rdnap.nl/download/coor-en-proj.zip, p. 44 (left)
http://www.rdnap.nl/download/rdnaptrans.pdf, p. 33 (right)

Jan