[PROJ] Ellipsoidal version of the gnomonic projection

[Charles Karney]

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...

-- 
Charles Karney <charles at karney.com>
702 Prospect Ave
Princeton, NJ 08540-4037