Physically Based Rendering, 3rd Edition

8.4.4: The torrance–sparrow model

An early microfacet model was developed by Torrance and Sparrow (1967) to model metallic surfaces. They modeled surfaces as collections of perfectly smooth mirrored microfacets. Because the microfacets are perfectly specular, only those with a normal equal to the half-angle vector,

${\omega }_{\mathrm{h}}={\omega }_{\mathrm{i}}\widehat{+}{\omega }_{\mathrm{o}}\text{,}$

cause perfect specular reflection from ω_i to ω_o (Figure 8.19).

Figure 8.19 For perfectly specular microfacets and a given pair of directions ω_i and ω_o, only those microfacets with normal ${\omega }_{\mathrm{h}}={\omega }_{\mathrm{i}}\widehat{+}{\omega }_{\mathrm{o}}$ reflect light from ω_i to ω_o.