[Proj] +towgs84 approximation error

[Martin Desruisseaux]

Hello Jochem and all

I think you already know that, but just for information for people
reading this thread that may be interested. Jochem shows below an
example of two steps using WGS84 as a hub (A to WGS84 to B) that are
mathematically combined for producing a single step going directly from
A to B. What we call "late-binding" goes a little step further in that
it is not just a mathematical combination. The 7-parameters for a datum
shift from A to WGS84 are derived by minimizing the errors in a set of
stations (like a "curve fitting"), and the 7-parameters for a datum
shift from WGS84 to B are derived by another "curve fitting". The
mathematical combination of the two is not exactly the same than what we
get if we do a "curve fitting" directly from A to B. Since those
parameter values can not be inferred mathematically from the "+towgs84"
parameters, they have to be stored in a separated table in the EPSG
database.

I'm not completely sure that I understood correctly the context, but it
may be that Jochem's intend could be understood not as improving a datum
shift operation, but rather as defining a Derived CRS in ISO 19111 sense
[1]. It doesn't make a difference for Proj.4 in its current state, but
if Proj.4 is someday upgraded to a "late-binding" implementation this
little nuance would need to be kept in mind.

    Regards,

        Martin


[1] http://portal.opengeospatial.org/files/?artifact_id=39049 section
B.1.2.2 at page 63.


Le 23/03/2017 à 13:49, Jochem a écrit :

> The "late-binding" will not solve these problems, since also for parameters
> between system A and B the rotation angles are too large for the approximate
> formulas:
>
> In my case:
>
> Frame A -> WGS84
> -294.1985,231.0171,-285.2462,-11.34441,40.54620,-9.73364,15.7901
>
> WGS84 -> Frame B
> 270.4047,-127.0720,286.7425,+11.13087,-1.67806,-24.24971,0.4536
>
> Frame A - > Frame B
> -23.764,103.995,1.506,-0.21346,38.86867,-33.98116,16.2437
> NB: I did not simple add the parameters, but used strict formulas to combine
> them.
>
> Therefore, I'm still convinced that the formulas of +towgs84 should be
> corrected.