[PROJ] Ellipsoidal version of the gnomonic projection

Wed Dec 28 13:59:14 PST 2022

Mathematically correct is not necessarily LEGALLY correct.  For instance with regard to France and to many French colonies, the French Army Lambert Truncated Cubic Conic is only partially conformal, but is a perfectly LEGAL projection for computing cadastral boundaries BEFORE 1948.  After 1948, the French Legislature changed the Law to require the perfectly conformal mathematical equations for France, and many French colonies followed suit - except for Algeria.

Mathematical elegance is nice but not always correct under the Law for a particular place.  The EPSG tries to pay attention to that; I am not so sure about ESRI.

Same goes for the many various truncations of the Transverse Mercator.  It depends on where and when for what equations.

Clifford J. Mugnier, c.p., c.m.s.

Chief of Geodesy,  (Emeritus)

LSU Center for GeoInformatics (ERAD 266)

Dept. of Civil Engineering

LOUISIANA STATE UNIVERSITY

Baton Rouge, LA  70803

Research:   (225) 578-4578

Cell:           (225) 328-8975

honorary lifetime member, lsps

fellow emeritus, asprs

member, apsg

________________________________
From: PROJ <proj-bounces at lists.osgeo.org> on behalf of Even Rouault <even.rouault at spatialys.com>
Sent: Wednesday, December 28, 2022 3:43 PM
To: charles at karney.com <charles at karney.com>; proj <PROJ at lists.osgeo.org>
Subject: Re: [PROJ] Ellipsoidal version of the gnomonic projection

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://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fgithub.com%2FOSGeo%2FPROJ%2Fpull%2F3522&data=05%7C01%7Ccjmce%40lsu.edu%7Ccd3df9623f73492cd90808dae91c9044%7C2d4dad3f50ae47d983a09ae2b1f466f8%7C0%7C0%7C638078606138115575%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=KQ9%2FVZ4BQb1XKztml3zCOeYSWMlK%2FyAfY0NaIkyCWHU%3D&reserved=0
>
> 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://nam04.safelinks.protection.outlook.com/?url=https%3A%2F%2Fdoi.org%2F10.1007%2Fs00190-012-0578-z&data=05%7C01%7Ccjmce%40lsu.edu%7Ccd3df9623f73492cd90808dae91c9044%7C2d4dad3f50ae47d983a09ae2b1f466f8%7C0%7C0%7C638078606138115575%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000%7C%7C%7C&sdata=D1Q2L9O6vA9mRVwlzX%2FWzmhfdLl5RHuIMU%2FdpU%2Fjels%3D&reserved=0
>
> 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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