The mathematical formula behind realistic metallic and dielectric surface reflections in PBR:

$$f_{\text{Cook-Torrance}} = \frac{D(N, H) \cdot F(V, H) \cdot G(N, V, L)}{4(N \cdot V)(N \cdot L)}$$

• $D$ (GGX Normal Distribution Function): Simulates microfacet roughness alignment.
• $F$ (Fresnel-Schlick): Increases reflectance at grazing viewing angles.
• $G$ (Smith Geometry Shadowing): Accounts for microfacets shadowing each other.

Energy-conserving: material reflections never exceed incoming light energy!

The Cook-Torrance BRDF with GGX distribution is what makes metallic and rough materials look indistinguishable from real life.

Clean mathematical breakdown.