[Proj] Lat-Lon values under different ellipsoides

Jan Hartmann j.l.h.hartmann at uva.nl
Fri Feb 6 09:18:52 EST 2009

As an addition, look how the British Ordnance survey solves the problem 
of converting Lat-Lon values from one ellipse to another:

" To summarise: for a simple datum change of latitude and longitude 
coordinates from datum A to datum B, first convert to Cartesian 
coordinates (formulae in annexe B) taking all ellipsoid heights as zero 
and using the ellipsoid parameters of datum A; then apply a Helmert 
transformation from datum A to datum B using equation (3); finally 
convert back to latitude and longitude using the ellipsoid parameters of 
datum B (formulae in annexe C), discarding the datum B ellipsoid height. "

This would mean that different lat-lon values for different ellipsoids 
are *derived* from projected coordinates, not the other way round, as I 
thought. I still don't get the relationship between those computed 
lat-lon values and the astronomical ones though.


Frank Warmerdam wrote:
> Jan Hartmann wrote:
>> Hi,
>> This is something I have long been banging my head against. I think it 
>> is a bug, but I am not sure. If I take a lat-lon value, computed on a 
>> particular ellipsoid, and convert it to the lat-lon value on another 
>> ellipsoid, I should get a different value, right? (e.g. cs2cs 
>> +proj=longlat +ellps=bessel +to +proj=longlat +ellps=WGS84). PROJ4 
>> always gives the same value, but I have an extensive list of coordinates 
>> of church towers in the Netherlands with their lat-lon values in 1850, 
>> based an a slightly smaller ellipsoid than we use nowadays, and the 
>> lat-lon of the same towers derived from our modern RD-system, based on 
>> the Bessel-ellipsoid, and without the WGS84 correction. There is a 
>> systematic difference of about 50 meters. If I do the same computation 
>> with the projected coordinates, I get the correct answer. Moreover, in 
>> that case the transformation changes when I change the 
>> ellipse-parameter, something that does not happen with lat-lon coordinates.
>> So, is this a bug in PROJ? If so, can someone with geodetic experience 
>> here explain to me how people can get different lat-lon values for the 
>> same point, based on astronomical measurements?
> Jan,
> As of PROJ 4.6.0, the policy is to not attempt any conversion of lat/long
> values between coordinate systems where only an ellipsoid is given.  So, to
> get a datum shift it is now necessary to provide some sort of datum
> shift information for both the source and destination coordinate systems.
> This is a deliberate change of policy to avoid lots of other complaints in
> the past.
> I would suggest using something appropriate like +datum=potsdam for your
> Bessel data, and +datum=WGS84 instead of +ellps=WGS84.
> Best regards,
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