We consider the Cook–Torrance bidirectional reflectance distribution function (BRDF), which is a physically based model of a reflecting surface. It assumes that a surface is a collection of planar microscopic facets—microfacets—with each microfacet acting as a perfectly smooth reflector. Accordingly,

,

where

,

which describes the distribution of microfacet orientations, with RMS as the root-mean-square slope of the microfacets; is the angle between the normal surface vector and the halfway angle vector (vector sum of the incident vector and the radiant vector at angle ); is the geometric attenuation factor that accounts for microfacet shadowing. The factor is in the range of 0 (total shadowing) to 1 (no shadowing). In this case, we have not considered either multiple reflection phenomena or shadowing, and it is determined as equal to 1. is a Fresnel reflection term related to the material’s index of refraction. Here again, it is determined to be equal to 1, consistent with the assumption that the surface is totally reflective [2].

The "Model" window shows the behavior of reflected rays when varying the surface roughness. The surface roughness has been modeled by randomly picking points from a normal distribution having a zero mean and a standard deviation equal to the RMS control. The "number of points" slider helps to get the microfacets closer or farther by increasing or decreasing the number of points considered on the axis. It is possible to increase the number of incident rays with the "beam diameter" slider, as well as to thicken them with the "beam intensity" slider.

The "Distributions" window shows the comparison of the theoretical Cook–Torrance distribution (colored orange) with the experimental one obtained using the "Model" window model (colored blue).