I wonder how bad microfacet normal distribution complexity impacts the runtime complexity of Monte Carlo samples. Mirrors are probably the easiest to sample comprehensively due to the fact that there's very few angles to sample (i.e. direct reflections). When we work with more complex surfaces, are there simplifications or approximations we can make about the surface distribution? What would happen if we did some texture mapping to actually map the surface itself physically instead of having some kind of normal distribution?
Sampling from the distribution is generally done with the inverse method, and so is not too computationally intensive. If we wanted to texture map a surface instead of sampling it, we would have to know the color of the surface already which would defeat the purpose of sampling the BRDF.
The unevenness of these surfaces reminds me a lot of bump mapping from when we discussed texture mapping--another really interesting example of how small changes to the surface indentation of a mesh (though performed here without changing the mesh itself) can make a world of difference. Does this reveal a larger trend in human perception, wherein a certain amount of character makes an image look real (but too much--like JPEG artifacts, excessive color in strange places, etc.--can ruin the illusion)? And how/would we apply bump mapping techniques here (perhaps how deep each bump is in the mesh to change the resulting normals)?
I also remember it being mentioned in lecture that these surfaces can be defined parametrically. Given the apparent variety in peaks here, how would we implicitly define or parametrize these sorts of surfaces?