[PROJ] Ellipsoidal orthographic: condition of projectability ?

[Even Rouault]

Hi,

In https://github.com/OSGeo/PROJ/pull/2361, I've implemented the ellipsoidal formulation 
of the orthographic projection from the formulas from EPSG guidance note 7-2, but one 
missing piece is the condition of projectability.

In the spherical formulation, there is a test to check that a given (lam, phi) is visible from the 
projection plane or not. 
https://github.com/rouault/PROJ/blob/2e104e092578347de11208e9a3a80a3bf711265d/
src/projections/ortho.cpp#L53
It seems it comes from https://pubs.usgs.gov/pp/1395/report.pdf equation (5-3), page 149

Looking at the formula, one can observe that it is actually the (opposite of the) partial 
derivative of y(lam, phi, phi0) with respect to phi0.
But perhaps this is just a coincidence due to the spherical case.

Now, the question... What about the ellipsoidal case:
- Should the exact same formula (Q->sinph0 * sinphi + Q->cosph0 * cosphi * coslam < - EPS10) 
of the spherical case be used as well ?
- Or should we compute the partial derivative of y(lam, phi, phi0) with respect to phi0 with 
the ellipsoidal formula of y from
https://github.com/rouault/PROJ/blob/2e104e092578347de11208e9a3a80a3bf711265d/
src/projections/ortho.cpp#L136 (will not be pretty...)
- something else ?

Even


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