BRDFmallinnus

BRDFmallinnus, or BRDF modelling, refers to the study and application of the Bidirectional Reflectance Distribution Function. The BRDF characterizes how light is reflected at a surface, describing how much of the incoming radiance from one direction is reflected into another direction.

Formally, the BRDF is a function f_r(ω_i, ω_r) that relates incident light from direction ω_i to reflected light in direction ω_r. For a differential incident irradiance dE_i from ω_i, the differential reflected radiance in ω_r is dL_r(ω_r) = f_r(ω_i, ω_r) L_i(ω_i) cos θ_i dω_i, where θ_i is the angle between ω_i and the surface normal. The BRDF has units of sr^-1 and satisfies reciprocity f_r(ω_i, ω_r) = f_r(ω_r, ω_i). Energy conservation imposes that, for every incident direction, the reflected flux does not exceed the incoming flux: ∫_Ω f_r(ω_i, ω_r) cos θ_r dω_r ≤ 1.

Common BRDF models range from simple to physically based. Lambertian models approximate purely diffuse reflection with f_r = ρ/π. More advanced diffuse models include Oren-Nayar, which accounts for roughness. Specular and glossy reflections are often described by microfacet models such as Cook-Torrance, which combine a microfacet distribution D, a Fresnel term F, and a geometry term G to capture roughness, angle dependence, and shadowing/m masking. Phenomenological shading, like Phong or Blinn-Phong, provides simple highlights with adjustable exponents.

BRDFs are central to rendering and material appearance in computer graphics and vision. They can be measured with gonioreflectometers, stored in BRDF databases, and used in physically based rendering to produce consistent, view-dependent surface appearance across wavelengths and lighting. Limitations include wavelength dependence, polarization, anisotropy, and spatial variation on real surfaces.