BRDFs model how a surface reflects light as a function of incoming and outgoing directions

The Bidirectional Reflectance Distribution Function (BRDF) describes how much light arriving from direction ω_i is reflected toward direction ω_o at a surface point, per unit solid angle. A BSDF (Bidirectional Scattering Distribution Function) extends this to include transmission (the BTDF). BSDFs are categorised by type: diffuse (uniform in all directions, Lambertian), glossy (concentrated reflection), and specular (delta-function mirror/refraction), and by direction (reflection vs. transmission). A material model is a composition of one or more BxDF lobes. In physically based rendering, BSDFs must satisfy energy conservation (total scattered energy ≤ incident) and reciprocity (Helmholtz reciprocity). The BSDF is evaluated inside the path tracer’s main integration loop to weight incoming radiance contributions.

Examples

Lambertian diffuse: f(ω_i, ω_o) = albedo/π (constant regardless of angle). Mirror specular: delta function — only one ω_i contributes to each ω_o. Conductor (metal): uses Fresnel equations, highly wavelength-dependent.

Assessment

For each material (matte clay, brushed aluminium, clear glass), identify which BxDF lobe types are needed and which parameter(s) differentiate them. Then sketch the lobe shape on a polar BRDF diagram.