The Orthographic-Aitoff Projection

[Atarimaster]

The large image you posted, Atarimaster, underlays precisely beneath the graticule I generated for the “pseudorthographic”. It really is the same projection.

However, the smaller image is wrong. The outer perimeter is not an ellipse. It has been trimmed in some odd way.

Uuuh, I screwed up and accidently removed the outer border of the small equatorial image. On the image provided here, I changed that.
Or did I get you wrong now and you’re talking about the other small image (the tilted one)?

There is something more going on here. I do not think G.Projector is behaving well. Does it have a perspective distance parameter, and does that change when you recenter the projection?

No, G.Projector’s parameters change depending on the projection you selected, and for Raisz Half Ellipsoidal it only offers to change the central meridian and the tilt angle.

[daan]

However, the smaller image is wrong. The outer perimeter is not an ellipse. It has been trimmed in some odd way.

Uuuh, I screwed up and accidently removed the outer border of the small equatorial image. On the image provided here, I changed that.
Or did I get you wrong now and you’re talking about the other small image (the tilted one)?

I mean the tilted image. It does not have an elliptical boundary, and it does not represent the entire sphere.

— daan

[Atarimaster]

I mean the tilted image. It does not have an elliptical boundary, and it does not represent the entire sphere.

Umm, yes, but that’s also true for the image you linked to (this one). And in the not-tilted version, it gets an ellipse, just like the Armadillo looks very much like Eckert IV when it’s not tilted – see this document, page 3/4 (which is a PDF-printed document from Furuti’s progonos.com, that I saved some time ago, before the site went offline).

It’s now 3:10 a.m. over here, so that’s Good Night for me!
Regards,
Tobias

[daan]

I see. The “tilt” itself must be part of the projection formulæ, in which case I would not call it “tilt” at all, but something like “vantage”. I had taken this “tilt” to mean a coordinate rotation, but clearly it is not.

Under this condition I can see that, in equatorial aspect •and• when projected from an equatorial vantage, the two projections are identical.

— daan