I was wondering if there was a definition of roughness for glossy/microfacet BRDFs, as this could be useful to a lot of stuff in one of my renderers. Fx
- An SPPM integrator bases the decision about whether or not to gather photons or continue tracing on the materials roughness. I have seen others do this based on GGX's roughness parameter or Blinn's exponent, but manually tweaking it for each BSDF is going to be a pain.
- Initializing a microfacet BRDF from a unified roughness term would make a renderer more robust wrt changing material definitions. The same roughness would lead to approximately the same visual result across multiple BRDFs.
- Image space lighting could also benefit from it. Instead of convoluting an image with all possible BRDFs, simply convolute it using some distribution (spherical gaussian) and use roughness to map between that distribution and the BRDF.
In the Physically Based Area Lights chapter in GPU Pro 5 they mention that Beckmann and Spizzichino, 1963, defines roughness for the Beckmann distribution as the "root mean square of the specular cone slope." ... whatever that means, but it sounds somewhat akin to the standard deviation, which would make it easy to map between any BRDF and a spherical gaussian.
Does anyone have any input on this subject? Good definitions of roughness or sources for some further research?
Ninja-edit: I forgot to mention what we've thought of so far. Mapping a BRDF as best as possible to a spherical gaussian and then using the 'sharpness' of that curve as the definition.