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

Jan Hartmann j.l.h.hartmann at uva.nl
Wed Jan 27 07:28:03 EST 2010

Thanks Mikael. Looks like I made an error with the rotation signs. Your 
PROJ parameters in (C) are the right ones. My faulty version (B) was 
taken over from the EPSG file in the latest (4.7) PROJ, which should be 
corrected too. I don't know how the parameters in the epsg-file are 
derived form the EPSG database, but in this case, the derivation isn't 

The whole problem of datum conversions is a permanent pain in the head, 
to express it mildly. Contributions like yours should be stored in some 
sort of central place, e.g. a Wiki, instead of lying around all over the 
Internet, together with all kind of faulty comments (like mine). Perhaps 
you should have a look at http://trac.osgeo.org/metacrs/, and think 
about setting up such a wiki about datum conversions, not only from and 
to WGS84, but also for other historical datums.

Thanks for the trouble you have taken,


On 25-1-2010 10:20, Mikael Rittri wrote:
> Jan, you wrote:
> > As I said in a previous email:
> >
> > http://www.ngi.be/FR/FR4-4.shtm
> Thanks.
> 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
> www.carmenta.com
> ------------------------------------------------------------------------
> *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:
> http://www.ngi.be/FR/FR4-4.shtm
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