[PROJ] Calculating meridian convergence

[Roger Oberholtzer]

It seems I made a mistake in my checking of the calculation.

It is the case that this works:

     proj_create(0, "proj=tmerc lon_0=15 k_0=0.9996 x_0=500000 ellps=GRS80");

and this does not work:

     proj_create(0, "EPSG:3006");

I don't know how I made that mistake. Sorry.

The thing is, we have been moving to using the EPSG codes in our
software. For various reasons. Mainly it is more general, and users
understand these codes.


Is this (using EPSG codes) something that is expected to work in this
context, but is just currently incorrect? Or is this something that
will probably never work?




On Wed, Jun 1, 2022 at 3:02 PM Roger Oberholtzer
<roger.oberholtzer at gmail.com> wrote:
>
> On Wed, Jun 1, 2022 at 1:27 PM Even Rouault <even.rouault at spatialys.com> wrote:
> >
> > Roger,
> >
> > I believe the issue here is that you use a transformation pipeline that
> > expects input coordinates to be in degrees.
> >
> > You should just use your code with
> >
> > PJ* proj = proj_create(0, "EPSG:3006");
>
> I tried that, and it did not help:
>
> proj_create(0, "EPSG:3006");
>
> LAT 55.600783
> LONG 13.100962
> angular_distortion 3.141593
> meridian_parallel_angle -89.999999
> meridian_convergence -1.543445
>
> LAT 58.618118
> LONG 15.468616
> angular_distortion 3.141593
> meridian_parallel_angle -89.999999
> meridian_convergence -1.577779
>
> I also tried a suggestion in a different answer here, and it did not help:
>
> proj_create(0, "proj=tmerc lon_0=15 k_0=0.9996 x_0=500000 ellps=GRS80");
>
> LAT 55.600783
> LONG 13.100962
> angular_distortion 0.000000
> meridian_parallel_angle 89.999999
> meridian_convergence -0.027351
>
> LAT 58.618118
> LONG 15.468616
> angular_distortion 0.000000
> meridian_parallel_angle 90.000000
> meridian_convergence 0.006982
>
> Both methods gave different results.
>
> I think the calculation should be
>
> γ = arctan [tan (λ - λ0) × sin φ]
>
> where
>
> λ is the longitude
> λ0 is the central meridian of the projection
> φ is the latitude
>
> So, an alternative question is: is there a way to find the central
> meridian in a PJ CRS? Or wherever I would look for it in proj?
>
> >
> > Even
> >
> > Le 01/06/2022 à 11:49, Roger Oberholtzer a écrit :
> > > I am trying to determine the meridian convergence for a point. The
> > > projection is defined as:
> > >
> > > PJ *proj = proj_normalize_for_visualization(0,
> > >             proj_create_crs_to_crs(0, "EPSG:4326", "EPSG:3006", 0));
> > >
> > > The source lat/longs are wgs84 from a GPS receiver. The projection is
> > > Sweref99. That is working just fine. In my case, the LONG/LAT are in
> > > degrees.
> > >
> > >         PJ_COORD ivals, vals;
> > >         vals.xyz.x = LONG;
> > >         vals.xyz.y = LAT;
> > >         vals.xyz.z = HEIGHT;
> > >         ivals = proj_trans(tinfo->Proj, PJ_FWD, vals);
> > >
> > > So far, so good.
> > >
> > > I need to do some rotations of the projected points. Towards that end,
> > > I would like to determine the meridian convergence. I am expecting to
> > > use this as a correction to a yaw value that my GPS receiver also
> > > provides via an integrated IMU.
> > >
> > >         PJ_FACTORS factors;
> > >
> > >         vals.lp.lam = proj_torad(LONG);
> > >         vals.lp.phi = proj_torad(LAT);
> > >
> > >         factors = proj_factors(tinfo->Proj, vals);
> > >
> > > I must be doing something incorrectly, as I get similar results for
> > > data from different locations. Or I am missing a step. Or I am just
> > > doing something totally wrong.
> > >
> > > Data from west of the Sweref99 central meridian (convergence should be
> > > -1.56713° according to the Swedish authority):
> > >
> > > LAT 55.600783
> > > LONG 13.100962
> > > ALT 13.463000
> > > E 380351.081178
> > > N 6163285.609844
> > > angular_distortion 0.567652
> > > meridian_parallel_angle 1.570796
> > > meridian_convergence -0.004468
> > >
> > > Data from east of the Sweref99 central meridian (convergence should be
> > > 0.40007° according to the Swedish authority):
> > >
> > > LAT 58.618118
> > > LONG 15.468616
> > > ALT 79.686000
> > > E 527220.410693
> > > N 6497625.569591
> > > angular_distortion 0.645715
> > > meridian_parallel_angle 1.570796
> > > meridian_convergence -0.004696
> > >
> > > angular_distortion, meridian_parallel_angle, and meridian_convergence
> > > are the values returned by proj_factors().
> > >
> > > This is with proj 8.2.1 on Linux. It is generally working fine. It's just this.
> > >
> > > Any pointers would be greatly appreciated.
> > >
> > --
> > http://www.spatialys.com
> > My software is free, but my time generally not.
> >
>
>
> --
> Roger Oberholtzer



-- 
Roger Oberholtzer