[ S(x_i, \omega_i; x_o, \omega_o) = F(\eta, \omega_i) R_d(|x_i - x_o|) F(\eta, \omega_o) ]

For conductors (metals), V-Ray uses the ( \tilden = n + ik ), where ( k ) is the extinction coefficient:

[ D_GGX(m) = \frac\alpha^2\pi \left( (n \cdot m)^2 (\alpha^2 - 1) + 1 \right)^2 ]

Where ( \alpha = \textRoughness^2 ) (in V-Ray’s remapping). This distribution has a higher kurtosis than Beckmann, producing brighter specular cores and more pronounced falloff—critical for anistropic metals.

The ( G(l,v) ), using the Smith model (GGX variant), ensures energy conservation: