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How to find PDF to use with importance sampling

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I am not certain, but I think the formula in the link you refer to is a reformulation of the Phong NDF to account for light conservation (the formula used for normalized Phong specular BRDF).

Here is some material that might help you answer your question.

 

 

In the 1977 paper Models of Light Reflection for Computer Synthetized Pictures, James F. Blinn talks about several possible Facet Distribution Functions that can be chosen to build a Torrance-Sparow model of a specular BRDF:

NDFs.png

 

In the Global Illumination Compendium, Philip Dutré recalls the mathematical background of integration over the hemisphere:

integral_over_hemisphere.png

 

A derivation of the normalization factor for the Phong NDF has been given on Fabian Giesen site:

Normalization_Factor.png

 

 

 

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