I only know enough to be dangerous about this stuff. I'm no expert. I only suspect that the following are true:
1) The ideal curvature should only be purely horizontal, not vertical.
2) Circular curvature is only an approximation of the ideal parabolic shape, but probably close enough.
3) The projector would be at the focus of the parabolic arc, not at the center of the approximating circle.
4) The shape of the parabola would depend on the distance, zoom, and stretch factor.
Whether the focal plane is flat or curved might depend on the design of the lens. I don't know what my lens would do.
If the vertical and horizontal focal distances are very different, it could cause astigmatism.
I don't know enough to look at a lens design and understand its properties.
The focus problems might get trickier with larger lens aperture and chip size.
I found an interesting spreadsheet in this thread for calculating screen curvature:
It will be interesting to experiment with the lens when I get my projector - you know, for science.
I haven't read this, yet, but it looks interesting. Based on the title, he might prove me wrong about the torus.
edit: Never mind this one. He was just talking about reflection angles for high gain screens. A torus does seem ideal for that. I have noticed more curved (even torus) screens in theaters lately, possibly due to higher gain screens for digital projectors.Edited by rcohen - 10/1/13 at 12:49pm