### Multiplying microfacets/GGX

Posted:

**Fri Oct 11, 2019 8:28 am**Does anyone know if the product of two microfacet distributions (specifically GGX) is also a microfacet distribution and how to compute the alpha of the new distribution?

I found some conversion from alpha to standard deviation and used that along with the product of two gaussian distributions to derive an approximation of the combined alpha, but it ended up being aCombined^2 = a1^2 + a2^2, which I'm not a huge fan of, since I'll have to clamp aCombined back to 1 in some cases.

The use case is infinitely thin layered microfacet distributions. When the roughness of the outer layer changes, the roughness of the underlying layers should be changed to approximate rough transmission. But products of microfacet distributions would also just be a nice tool to have in the toolbox for the future.

I found some conversion from alpha to standard deviation and used that along with the product of two gaussian distributions to derive an approximation of the combined alpha, but it ended up being aCombined^2 = a1^2 + a2^2, which I'm not a huge fan of, since I'll have to clamp aCombined back to 1 in some cases.

The use case is infinitely thin layered microfacet distributions. When the roughness of the outer layer changes, the roughness of the underlying layers should be changed to approximate rough transmission. But products of microfacet distributions would also just be a nice tool to have in the toolbox for the future.