[Proj] Ellipsoid problem? Converting 1850 Dutch map to present day coordinate system

Jan Hartmann j.l.h.hartmann at uva.nl
Thu Dec 11 10:20:07 EST 2008

Thanks Janne. See the result of shifting the map 50M south:


Errors are smaller, but he map is still not as good as it could be. All 
arrows now point more or less at Amsterdam, which is nice, but not as it 
should be :-). The problem is that the errors are not linear in x or y, 
but are distributed more or less in concentric circles round the point 
of origin. It certainly has something to do with the ellipsoid used.

Oh, and by the way, if I change the ellipsoids in the cs2cs string 
below, results are different, as they should be. However, if I use the 
same method with latlon coordinates, results are the same, regardless of 
the ellipses used. Is this as it should be? Latlon values on the Bessel 
ellipsoid are different from latlon values on another ellipsoid, aren't 
they? At least the latlon values recorded in 1850 are significantly 
different from the modern latlon values for locations that are 
physically the same in both years.


support.mn at elisanet.fi wrote:
> Hello,
> the problem might be due to using wrong projection origin for some
> of the projections, since that usually also shifts the points. You might
> experiment by moving one of the latitude or longitude origins one at a
> time and then examining the results. When they start to minimize you
> are moving to the right direction with the origin.
> Regards: Janne.
> ---------------------------------
> Jan Hartmann [j.l.h.hartmann at uva.nl] kirjoitti:
>> Hi
>> Sorry to bother you again with my Dutch maps, but perhaps someone 
>> with more mathematical insight than I have can help. I am 
>> reprojecting about 650 control points from the official Dutch 
>> projection from  1850 (TMK), to the the present projection (RD). The 
>> coordinates of all points are known in both systems.  When I use 
>> cs2cs to project the points from the old system to the new,  the 
>> computed points  are 30-80 meters away from the official ones. See
>> http://mapserver.sara.nl/tmk/tmk1850_to_rd1970.png
>> There is some random error here, but most of the deviations look 
>> systematic to me. The 1850 had its central meridian over Amsterdam, 
>> and the arrows point to that central meridian. Could this possibly  
>> be an ellipsoid-related problem, and if so, how do I compute a better 
>> proj-string? It's not a Datum problem: the 1850 latlon coordinates 
>> and the corresponding present WGS84 coordinates are also know:
>> http://mapserver.sara.nl/tmk/latlon_1850_to_latlon_wgs84_1970.png
>> and they give completely different and much larger deviations.
>> Any hints would be appreciated. I've been using the following 
>> parameters, based on the official documentation from both periods:
>> cs2cs -E -f "%6.0f"  \
>>      +proj=bonne +lat_1=51.5 +lon_0=4.8838828  \
>>      +units=m +no_defs \
>>      +a=6376950.4 +rf=309.65  \
>>  +to +proj=sterea +lat_0=52.15616055555555 +lon_0=5.38763888888889 \
>>      +k=0.999908 +x_0=155000 +y_0=463000 \
>>      +units=m +no_defs  \
>>      +ellps=intl
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