Open peterkutz opened 2 months ago
This could be reasonably left as an exercise for the reader perhaps..
Though if you have a derivation of the result Peter, would be handy.
This was first suggested and derived by @Reedbeta :
Using the syntax from the ASM technical document, given
F_F82Tint(θ) = r + (1 − r)(1 − cosθ)⁵ − bcosθ(1 − cosθ)⁶
the cosine-weighted hemispherical average of that works out to be
r + (1 - r)/21 - b/126
This can be derived like this in Wolfram Alpha:
integrate (r + (1 − r)(1 − cosθ)⁵ − bcosθ(1 − cosθ)⁶) * cos(θ) * sin(θ) / π from theta = 0 to π/2 and phi = 0 to 2π
It is possible to analytically calculate the average albedo of the F82-tint model used for metal reflectivity in OpenPBR. Specifically, the average Fresnel can be calculated by integrating the reflectivity over the cosine-weighted hemisphere.
The average Fresnel is very useful to more accurately tint the multiple-scattering component of the rough metal surface. So I propose that we include this formula in the spec.