Could you explain more why the isotropic assumption means we only need the 3 inputs listed as the bottom of the slide, as compared to before when we needed all 4?
motoole2
Absolutely. The isotropic assumption means that I can rotate a surface about its normal, and it will produce the same BRDF response. In other words, $f(\theta_i, \phi_i, \theta_r, \phi_r)=f(\theta_i, \phi_i + a, \theta_r, \phi_r + a)$ for all values $a$. So by picking the value $a = -\phi_r$, I can reduce this function down to one of only 3 variables: $f(\theta_i, \phi_i, \theta_r, \phi_r)=f(\theta_i, \phi_i - \phi_r, \theta_r, 0)$ (since the fourth argument is always $0$).
Could you explain more why the isotropic assumption means we only need the 3 inputs listed as the bottom of the slide, as compared to before when we needed all 4?
Absolutely. The isotropic assumption means that I can rotate a surface about its normal, and it will produce the same BRDF response. In other words, $f(\theta_i, \phi_i, \theta_r, \phi_r)=f(\theta_i, \phi_i + a, \theta_r, \phi_r + a)$ for all values $a$. So by picking the value $a = -\phi_r$, I can reduce this function down to one of only 3 variables: $f(\theta_i, \phi_i, \theta_r, \phi_r)=f(\theta_i, \phi_i - \phi_r, \theta_r, 0)$ (since the fourth argument is always $0$).