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### #ActualCryZe

Posted 26 February 2013 - 06:37 AM

Have I thought about this all wrong? Or does reciprocity really break down when diffusers and Fresnel's laws are combined?

I think Helmholtz reciprocity doesn't apply to diffuse light at all, because diffuse light actually is the same as subsurface scattering, just in such a small scale, that one can approximate it by evaluating it at the entrance point. Diffuse light is the light scattering inside the surface, which is simply specular reflection thousands of times inside the surface. Helmholtz reciprocity isn't supposed to be correct for this process, because it's not just a single reflection. But it works for all the little specular reflections inside the material and the "macro" specular reflection on the surface.

And it works for cook torrance:

The halfway vector is the same whether you calculate it from (L+V)/length(L+V) or (V+L)/length(V+L), and thus the microfacet distribution function returns the same value, since it relies on NDotH. Fresnel relies on LDotH, but that's the same as VDotH. And the geometric term is the multiplication of the "sub geometric term", one time calculated for NDotV, and one time calculated for NDotL, and since scalar multiplication is commutative, the result is the same whether you switch NDotV and NDotL, or not. The same applies to the NDotL * NDotV in the denominator of cook torrance.

### #2CryZe

Posted 26 February 2013 - 06:30 AM

Have I thought about this all wrong? Or does reciprocity really break down when diffusers and Fresnel's laws are combined?

I think Helmholtz reciprocity doesn't apply to diffuse light at all, because diffuse light actually is the same as subsurface scattering, just in such a small scale, that one can approximate it by evaluating it at the entrance point. Diffuse light is the light scattering inside the surface, which is simply specular reflection thousands of times inside the surface. Helmholtz reciprocity isn't supposed to be correct for this process, because it's not just a single reflection. But it works for all the little specular reflections inside the material and the "macro" specular reflection on the surface.

### #1CryZe

Posted 26 February 2013 - 06:29 AM

Have I thought about this all wrong? Or does reciprocity really break down when diffusers and Fresnel's laws are combined?

I think Helmholtz reciprocity doesn't apply to diffuse light at all, because diffuse light actually is the same as subsurface scattering, just in such a small scale, that one can approximate it by evaluating it at the entrance point. Diffuse light is the light scattering inside the surface, which is simply specular reflection thousands of times inside the surface. Helmholtz reciprocity isn't supposed to be correct for this process, because it's not just a single reflection. But it works for all the little specular reflections and the specular reflection on the surface.

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