[PROJ] "Local" projection method?

[Even Rouault]

On jeudi 24 septembre 2020 11:01:22 CEST Even Rouault wrote:
> On jeudi 24 septembre 2020 05:42:22 CEST Kristian Evers wrote:
> > Nyall,
> > 
> > > Based on this, would it be appropriate to directly map this projection
> > > method across to the "Orthographic" method? Or am I missing something
> > > important?…
> > 
> > Yes, it would seem so. Be aware though, the current Orthographic
> > projection
> > implementation in PROJ is only valid in the spherical case. You would have
> > to extend that to the ellipsoidal case for the mapping described by Esri.
> > We’ve got an old issue [0] which contains some hints on how to go about
> > that.
> 
> "Recent" EPSG guidance note 7.2
> 
> https://drive.tiny.cloud/1/4m326iu12oa8re9cjiadxonharclteqb4mumfxj71zsttwkx/
> 62018e48-9da4-43e7-b598-1202cd96ec9f
> 
> (link got from epsg.org)
> 
> has the maths for the ellipsoidal formulation of the orthographic projection
> in paragraph 3.3.5, page 89

I gave this a try at https://github.com/OSGeo/PROJ/pull/2361
with mapping from ESRI WKT Local to +proj=ortho

> 
> I cannot comment on the full equivalence of the "Local" projection, but
> hopefully in the Scale_Factor=1 + Azimuth=0 case, they would match.
> 
> One way to check that the theory local = ortho on the sphere is valid would
> be to use ArcGIS with a sphere as the ellipsoid and compare results with
> +proj=ortho

I get now with
https://lists.osgeo.org/pipermail/proj/2020-September/009827.html
the expected result of
https://lists.osgeo.org/pipermail/proj/2020-September/009825.html

echo "22000 77000 0" | src/cct -d 8 +proj=pipeline +step +inv +proj=ortho +lat_0=41.329238 
+lon_0=69.295403 +x_0=24547.608 +y_0=76540.608 +ellps=krass +step +proj=push +v_3 
+step +proj=cart +ellps=krass +step +proj=helmert +x=25 +y=-141 +z=-78.5 +rx=0 +ry=-0.35 
+rz=-0.736 +s=0 +convention=coordinate_frame +step +inv +proj=cart +ellps=WGS84 +step 
+proj=pop +v_3 +step +proj=unitconvert +xy_in=rad +xy_out=deg +step +proj=axisswap 
+order=2,1
  41.33356081    69.26421906    0.00000000           inf

Which is indeed the same result as with +proj=tmerc, due to the point being close to the 
projection center.

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