I don't understand what's going on in this formula. What is the output here?
I believe this formula is describing f_r as follows. Basically, the output is 0 unless...
(cos theta_i = cos theta_o) and | phi_i - phi_o | = pi
If so, then we get that f_r is 1 / (cos theta_i).
This makes sense because we only want an output when the reflection is perfect.
@Ken It's a BRDF, so it is describing the ratio of reflected radiance (in a particular direction) to incident irradiance (from a particular direction). More specifically, ignoring the cosine theta denominator term, we can consider this to be an indicator function that produces 1 when the incident and outgoing directions represent a specular reflection (the outgoing direction = the incident direction reflected about the surface normal), and 0 otherwise.