[Proj] Belge 1972 / Belgian Lambert 72 (31370) - towgs84parameters

Mikael Rittri Mikael.Rittri at carmenta.com
Mon Jan 25 04:20:07 EST 2010

Jan, you wrote:

> As I said in a previous email:
> http://www.ngi.be/FR/FR4-4.shtm
This page does not specify the rotation sign convention, as far as I could see, 
but I downloaded the converter.  Then I tried to convert the sample point 2°30' E, 51°N 
(west Belgium) from BD72 to WGS84, and compared the results with PROJ.4.
(A) Older transform, according to Jan.
    FWTools2.2.8> cs2cs +proj=longlat +ellps=intl +towgs84=-99.059,53.322,-112.486,0.419,-0.830,1.885,-1 +to +proj=longlat +datum=WGS84
    2.5 51
    2d30'4.369"E    50d59'58.092"N 41.378
(B) Newer transform according to Jan, assumes www.ngi.be/FR/FR4-4.shtm <http://www.ngi.be/FR/FR4-4.shtm>  uses Position Vector Transform:
    FWTools2.2.8> cs2cs +proj=longlat +ellps=intl +towgs84=-106.8686,52.2978,-103.7329,-0.3366,0.457,-1.8422,-1.2747 +to +proj=longlat +datum=WGS84
    2.5 51
    2d30'1.464"E    50d59'57.151"N 41.359
(C) Newer transform, but assuming that www.ngi.be/FR/FR4-4.shtm <http://www.ngi.be/FR/FR4-4.shtm>  uses Coordinate Frame Rotation:
    FWTools2.2.8> cs2cs +proj=longlat +ellps=intl +towgs84=-106.8686,52.2978,-103.7329,0.3366,-0.457,1.8422,-1.2747 +to +proj=longlat +datum=WGS84
    2.5 51
    2d30'4.373"E    50d59'58.093"N 41.455
(D) Result from Dutch converter, downloaded via www.ngi.be/FR/FR4-4.shtm <http://www.ngi.be/FR/FR4-4.shtm> 
    2°30'04.37266" E,  50°59'58.09273" N  
Distance (A) to (D):  0.08 m
Distance (B) to (D): 63.75 m 
Distance (C) to (D):  0.01 m 
(all measured by http://williams.best.vwh.net/gccalc.htm)
I conclude that www.ngi.be/FR/FR4-4.shtm <http://www.ngi.be/FR/FR4-4.shtm>  uses the Coordinate Frame Rotation, just like 
EPSG says in EPSG:15929, "BD72 to WGS 84(3)", and therefore, the three rotation
angles should be reversed when constructing a +towgs84 clause for PROJ.4, as in (C) above.
(EPSG has in fact reversed all parameter signs given in FR4-4, but that's because FR4-4 gives 
 the parameters _from_ ETRS89 (or WGS84) _to_ BD72.)  
Best regards,

Mikael Rittri
Carmenta AB


From: Jan Hartmann [mailto:j.l.h.hartmann at uva.nl] 
Sent: Friday, January 22, 2010 4:04 PM
To: Mikael Rittri
Cc: PROJ.4 and general Projections Discussions; Thibaut Gheysen
Subject: Re: [Proj] Belge 1972 / Belgian Lambert 72 (31370) - towgs84parameters

On 22-1-2010 15:40, Mikael Rittri wrote: 

	Jan, you wrote 
	> All my observations about the towgs parameters have been tested with real Belgian coordinates overlaid over Google.
	Fine.  But if you did make an error when transcribing the newer transforms into Proj.4 syntax, and 
	the error was just in the rotation angles, then the effect may be too small to notice.  
	I mean, the angles describe a rotation, so there is presumably a fixed point in Belgium where 
	the rotation has no effect.  If your test points happened to be near the fixed point, the 
	effect of the reversed angle signs could be very small.  
	> As I said before, the EPSG database is not very systematical in the way it represents its formulas, 
	> it just takes them from whatever source is available, untested AFAIK. Never use them without testing them with real world coordinates.
	I agree completely.  But I am not yet convinced that you are right and EPSG wrong for the newer transforms,
	although that is certainly possible.  Do you have some link to the offician Belgian documents? 

As I said in a previous email:


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