## Re: [Algorithms] approximation to pow(n,x)?

 Re: [Algorithms] approximation to pow(n,x)? From: Jon Watte - 2009-11-11 04:24:42 ```But that's equally true for the reflection vector! If all the micro-mirrors 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 half-angle 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 half-angle 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 half-angle 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 wrote: > The half-angle formulation is not just more physically correct than the > reflection-vector formulation, it is fundamentally more meaningful. ... > The half-vector 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. ```