> You are right, when I look at it, it is essentially equal to a perspective
> camera (except inside out, which isn't possible with a regular camera except by
> using refractive lenses).  But this is exactly how I understood it from
> wikipedia, each ray passes from the opposite pole, straight through the sphere
> surface, onto the projection plane.  To me it appears that is supposed to be
> exactly equale to a perspective projection (with a 90deg viewing angle), but
> that it is traditionally meant as a means of projecting a spherical surface
> onto a flat surface.  We are thinking of it as 3d objects rather than 2
> surfaces which I think confuses the matter in our interpretation.

Right. If the scene is entirely contained in the (surface of) the sphere,
then a perspective camera suffices. The original poster wanted something
different, though: To apply this kind of projection after the scene has
been projected to the sphere. So, the camera must provide two projections
at once, giving importance to the angle at which a ray of vision hits the
sphere.

  Mark Weyer

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