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Where is the additional 1/N factor in the environment map prefiltering code?

When prefiltering the environment, an assumption is made that the two factors in the integrand of the radiance integral are uncorrelated, such that the integral can be simplified into the product of two integrals (see equations 6 and 7 in the Real Shading in Unreal Engine 4 paper).

The number of samples of the first and second term are chosen independently of each other, and I expect that both sums will be appropriately normalized by how many samples are taken.

Looking at UnrealEngine/Engine/Shaders/PostProcessAmbient.usf, I see a divide by NumSamples in the function IntegrateBRDF (the second term) but not in PrefilterEnvMap where we perform the convolution of the environment map with the GGX lobe.

Am I missing something regarding the math here? I'm trying to see if the additional 1/N term is hiding somewhere (like in the convolution or cosine weighting or something) and I'm not seeing it.

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asked Mar 11 '15 at 11:07 PM in Rendering

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