[PROJ] Latitude of natural origin in Transverse Mercator

[Javier Jimenez Shaw]

Thanks Even.
I also reached the article in the Wikipedia, but I couldn't find the
meaning of "m" in "m(phi0)
Then I went to PROJ code. In the simplified version it was kind of clear
that they were equivalent, but got very confused with the notation, and
didn't know what is pj_mlfn (thanks for the tip). I downloaded "map
projections a working manual" from USGS, and the formulas are a bit
different, that confused me even more (I hope they are equivalent ;)
That pushed me to ask here.

Cheers.
.___ ._ ..._ .. . ._.  .___ .. __ . _. . __..  ... .... ._ .__
Entre dos pensamientos racionales
hay infinitos pensamientos irracionales.



On Fri, 13 Jan 2023 at 16:13, Even Rouault <even.rouault at spatialys.com>
wrote:

> Hi Javier,
>
> interesting. Quick numerical experimentation seems to confirm that they
> are "equivalent", as well as looking at the drawing of how the projection
> is built.
>
> And looking at the maths of the approximate ellipsoidal forward method in
> src/projections/tmerc.cpp, one can see:
>
> xy.y = P->k0 * (.... - Q->ml0 + ....... )
>
> (the false northing value is added in generic PROJ code)
>
> where
>
> Q->ml0 = pj_mlfn(P->phi0, sin(P->phi0), cos(P->phi0), Q->en);
>
> where pj_mlfn() computes the meridional distance (formula in src/mlfn.cpp)
>
> So - P->k0 * Q->ml0 should be the value of the false northing equivalent
> to the effect of phi0. (I believe :-))
>
> Also confirmed by the formula N=N0 +y(lam,phi) - k0 * m(phi0) of
> https://en.wikipedia.org/wiki/Transverse_Mercator_projection#Coordinates,_grids,_eastings_and_northings
>
> Even
> Le 13/01/2023 à 15:28, Javier Jimenez Shaw a écrit :
>
> Hi
>
> I have a question about Transverse Mercator.
> What is the impact of the parameter "Latitude of natural origin",
> compared with the "False Northing"? (apart from the fact that one is in
> degrees and the other in meters)
> Is there any difference on using a Latitude of natural origin of, let's
> say, 40 degrees, or compute the equivalent False Northing?
>
> Thanks.
> Javier
> .___ ._ ..._ .. . ._.  .___ .. __ . _. . __..  ... .... ._ .__
> Entre dos pensamientos racionales
> hay infinitos pensamientos irracionales.
>
>
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