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Mixing correctly image based lighting with classical lighting

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Image Based Lighring (IBL) is the use of pre-computed radiance and irradiance cubemap (for the actual most used at least).
My question is about to mix correctly IBL with classical lighting (PBR), meaning mix the result of radiance and irradiance sampling.
I tried multiple thing but i'm not sure how to achieve the most physically correct result :
1) LightingResult += DiffuseColor * Irradiance + Radiance * Reflectance
2) On each light do DiffuseFactor * Irradiance + SpecularFactor * Radiance * Reflectance
For the second version, the ambient light should do AmbientLight * Irradiance if i'm correct.
I'm not sure the first version is correct because then you always have one lighting and never have black result.
So, I guess the second version is more correct or a more correct calcule exists.

Edited by Alundra

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