From: Jon Watte <jwatte@gm...>  20091111 04:24:42

But that's equally true for the reflection vector! If all the micromirrors were perfectly flat, then an infinite specular power would be applied, and you'd get a perfect reflection of the lighting environment  in fact, this is what environment mapping gives you. As the mirrors start deviating from the perfectly flat state, the specular power would decrease, and the specular reflection area would grow in size. I don't see how you can say that the halfangle formulation is more meaningful. We're still talking about reflected light. In the perfectly reflected case, clearly the reflection vector is 100% meaningful and accurate, and any other formulation would be less meaningful. I don't see how "meaningfulness" would change as smoothness goes from 100% to 99.9% or 95% or 50%. I do agree that the math gives you a different assumed microfacet distribution in the case of the reflection formulation versus the halfangle formulation. Both are approximations, of course. However, what I don't get, is why the reflection vector approximation is considered so inferior to the more expensive halfangle vector approximation. Does it have anything to do with the space integral of the reflection cone formed by the vector in question spread out by the power function? If so, how? Sincerely, jw On Sun, Nov 8, 2009 at 9:41 AM, Nathaniel Hoffman <naty@...> wrote: > The halfangle formulation is not just more physically correct than the > reflectionvector formulation, it is fundamentally more meaningful. ... > The halfvector comes from microfacet theory. Imagine that the surface is > actually a large collection of tiny flat mirrors when viewed under > magnification. Recall that a mirror only reflects light in the reflection > direction. For given light vector L and view vector V, only mirrors which  Americans might object: there is no way we would sacrifice our living standards for the benefit of people in the rest of the world. Nevertheless, whether we get there willingly or not, we shall soon have lower consumption rates, because our present rates are unsustainable. 