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DX12 Magic Number 8 Used For Energy Conservation, One Reason ?

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I always seen pi used for energy conservation but recently in the frank luna dx12 book I saw magic number 8 used (he uses that from another book).

The full formula is :

float roughnessFactor = (m + 8.0f)*pow(max(dot(halfVec, normal), 0.0f), m) / 8.0f;

Any reason 8 is used here instead of the classical divide by pi ?


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