What does the notation f(... : ...) mean in this context? How do you go from a 4 parameter function on the left to a 3 parameter function on the right?
@rutajoshi It's not f(... : ...). It's f(... ; ...). In matematics, ";" is very similar to "," except that it helps to separate variables and parameters. In this context, it means, given theta r and phi r, f_r is a function of theta_i and phi_i.
Someone please correct me if I am wrong.
I feel like the first equality should be f_r(theta_i, phi_i; theta_r, phi_r)=f_r(theta_i, 0, theta_r, phi_r-phi_i), and the one who made this slide rewrite the RHS as f_r(theta_i, theta_r, phi_r-phi_i).
Anyway, the isotropic property means that no matter how you rotates incident & outgoing light, as long as their relative angle (difference in phi) keeps the same, the BRDF does not change.