My use of perpendicular was taken from your initial definition, it is a simplification. My second definition is probably more helpful and accurate. The use of reflected and dispersed light is only a metaphor and not a concrete definition. Actually what will happen is that gain will be the stated number at 0 degrees off the reflected path of light from the projector and the gain will fall off the father off axis you get. The brightest point will probably not be the exact center of the screen, instead it will be the point on the screen that your eyes are on-axis for.
You shouldn't use average gain, uniformity is more common. Most people (in the forum http://www.avsforum.com/ubb/smile.gif
)will recognize what you mean when you say you have a "2.0 gain screen," in that you have a screen that is twice as bright as a 1.0 gain, but that this effect will likely fall off at the edges of the screen. Instead of using average gain to describe the effects of a toroidal screen, you should probably use uniformity. In the context of a 2.0 gain toroidal screen this would mean that it would have a "uniform 2.0 gain surface". This would mean that a full white field you appear to be the same brightness at all points on the screen (and hopefully from all the viewing positions) with no fall off. In essence, it is directing more of the on-axis (or close to on-axis) light onto the audience as opposed to the walls and ceiling.
It is probably more accurate to view a toroidal screen as giving a high-gain screen greater uniformity rather than a higher "average gain".
What you are saying about the practical uses of a curved screen are not exactly true. A 50% increase in screen area will still require a 50% increase in light output or gain to maintain brightness. The advantage of the curved screen is that it will have better uniformity if you increase gain. However, in the context of your "average gain" your assertions are correct.
Don't you ever find it sad that the features that Faroudja charge such astronomical prices for are now reproduced at a fraction of the cost sometimes as little a year after introduction? The DVP-5000 will double 1080i, but I would argue that the current crop of video cards (at $150-500) may be able to do that (and with the same field-adaptive de-interlacing) and less than a year after the DVP-5k was intro'd. There is still a lot of value in the high quality components and the slightly better scaling and de-interlacing algorithms that Faroudja uses, but not at the horrendously inflated prices they charge.
...or I could just be jealous because I can't afford one http://www.avsforum.com/ubb/biggrin.gif