[PROJ] Ellipsoidal version of the gnomonic projection

[Even Rouault]

I'm favorable to this improvement. This isn't the first time we add an 
ellipsoidal formulation to a projection method that had only a spherical 
one (last time was for orthographic). As I mentioned in the PR, it would 
be great if we know how to deal with CRS definitions under the Esri 
authority that use gnomonic to hopefully be consistent with what they 
do, at least on CRS under their authority, as Esri has several flavors 
of gnomonic. Hopefully we'll get some input from Esri people. I'll try 
to reach with them.

Even

Le 28/12/2022 à 22:01, Charles Karney a écrit :
> I've submitted a pull request (PR)
>
>   https://github.com/OSGeo/PROJ/pull/3522
>
> for PROJ to implement an ellipsoidal generalization of the gnomonic
> projection.
>
> The spherical gnomonic projection has the property that geodesics map to
> straight lines.
>
> There's no projection with the same property for the ellipsoid.
> However, the spherical gnomonic projection is also the limit of a double
> azimuthal projection, a projection which preserves the azimuths from two
> points, in the limit that the two points coalesce.  This property
> carries over to the ellipsoidal version of the projection implemented by
> this PR.  For earth ellipsoids, geodesics which pass within a few
> hundred km of the center of the projection are very nearly straight.
> For details and for a derivation of the projection, see Sec. 8 of my
> 2013 paper
>
>   Algorithms for geodesics
>   https://doi.org/10.1007/s00190-012-0578-z
>
> Merging this PR will result in a minor incompatibility:  With the
> gnomonic projection in current version of PROJ, an ellipsoid is treated
> (inconsistently!) as a sphere whose radius matches the equatorial radius
> of the ellipsoid.  After the merge, the ellipsoidal gnomonic projection
> will be used (and you will get somewhat different results).   To retain
> the previous behavior you'll need to set the flattening of the ellipsoid
> to zero, +f=0.
>
> Comments are welcome...
>
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