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xguo

The BRDF is a distribution function because it tells you the probability that the light is reflected in a given direction. There's also the BTDF (where T stands for transmission) and if you combine the two, we get the BSDF (where S stands for scattering).

yenyu

More details of BRDF: https://en.wikipedia.org/wiki/Bidirectional_reflectance_distribution_function