[Proj] +towgs84 approximation error

Martin Desruisseaux martin.desruisseaux at geomatys.com
Wed Mar 22 17:25:46 EST 2017

Hello Jochem

The 7 parameter coordinate transformations are for datum shifts, which
are themselves approximative operations by nature. They have stochastic
error unrelated to the Proj.4 accuracy, much greater than the sine
approximation. For example the "NAD27 to WGS 84 (4)" transformation over
USA (EPSG:1173) has an accuracy of 10 metres. So in this context I
wonder what would be the purpose of aiming for an "accuracy" of 0.1 mm.
It can not be a positional accuracy (in the geodetic sense) at least,
but maybe the intend was something else?


Le 22/03/2017 à 22:41, Jochem a écrit :
> Hello, 
> I joined the mailing list because I noticed that the PROJ.4 library uses
> approximate formulas for the 7 parameter coordinate transformation defined
> by +towgs84 (technical details: The elements of the rotation matrix are the
> rotation angles instead of the product of sines and cosines of the angles).
> For really small rotation angles this gives the same result, but not for
> larger rotations. 
> For my current application I want to transform a map in QGIS with 1 mm
> accuracy. However, the approximation causes an error of 4 cm. Since PROJ.4
> normally gives results within 0.1 mm accuracy, I did not expect such
> approximation.
> What can I do to help to fix this?
> Regards, Jochem

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