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I'm reading a graphics book and it talks about BRDFs being the ratio between differential outgoing radiance and differential irradiance. The formula it gives is f(l, v) = dL(v)/dE(l) Where l is the light vector and v is the outgoing direction vector, and L is outgoing radiance and E is incoming irradiance.

But then the book says that for non area lights like directional and point lights, the BRDF can be expressed without differentials: f(l, v) = L(v) / E(l). How is this possible? The first formula seems to be a derivative, how do we get to this formula? What is the difference between non area and area lights that would allow us to arrive at this simplification?

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  • $\begingroup$ What book is that? Directional and point lights are described through Dirac deltas. $\endgroup$
    – lightxbulb
    Feb 10 '20 at 6:22
  • $\begingroup$ @lightxbulb Real-Time Rendering 3rd edition. Chapter 7 I think, in the BRDF section. $\endgroup$
    – Hachiko
    Feb 11 '20 at 21:51
  • $\begingroup$ Can you quote the relevant part? $\endgroup$
    – lightxbulb
    Feb 12 '20 at 5:01

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