On 2023-12-10 10:13 (-4), Bald Eagle wrote:
> 
> So, having looked into inversive geometry, stereographic projection, Mobius
> transforms, etc. - I think I recall seeing some examples of slightly different
> ways of projecting the sphere's surface onto a plane.

I suspect that there are an infinite number of such projections.

> Not having delved into this topic to any real extent, are there different image
> maps that might not result in a correctly mapped sphere?

It all depends on the projection algorithms.

> Or is the main problem just the cylindrical vs uv-mapping in the scene?

In this particular case, it's just cylindrical vs uv-mapping.  The
images were created in the equidistant cylindrical projection, so that
is what I had to work with.

> Also just curious if the sphere got scaled to be an oblate spheroid.

The sphere is not scaled.  To account for oblateness, I'd have to know
whether the maps were prepared with geocentric or geodedic latitudes,
and *then* I'd have to remember how I handled the difference 30 years
ago when I worked on USAF satellites.  And then a function would have to
be applied to distort the image map in the north-south orientation.

My head is already starting to hurt.

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