How does the Sigma value of the Cycles Velvet BSDF shader work? Intuitively, it seems to serve as some sort of ceiling value for the shading. How does it affect the light bouncing? I've looked at the ray diagram on the shaders page, which seems to show an away-from-center spread:
Is the sigma value related to the variance (in statistics, σ means variance) of the spread? Comparing the diagram to that of the normal distribution seems to indicate that this may be the case:
This would seem to mean that a σ-value of 0 makes the shader behave like a glossy shader, while a σ-value of 1 would make it behave like a diffuse shader; however, this does not appear to be the case.
I've prepared a video demonstrating a changing σ-value, from 0 to 1, on an actual velvety object for added realism.
Could one of the developers who understands what is going on identify the meaning here, mathematically or otherwise?