Irradiance is the energy of the incoming stream of light that impacts a surface at some point p. Radiance is the energy of the reflected light from p. These energy transfers are modeled using a bidirectional reflectance distribution function (BRDF). The material of the surface and its reflectance properties must be considered and is modeled with the appropriate function [48]. The geometry of the BRDF is

where all vectors are normalised. u is a vector in the surface plane. v is a vector in the surface plane orthogonal to u. n is the normal of the surface at p. β is the angle between n and h. The half vector h bisects the angle between the light source along ωi and view along ωo. Angle between ωi and n is θi. Angle between ωo and n is θo.

For some point p irradiated from all directions, the reflectance function determines the radiance coming from that point relative to some viewing direction. The function is