Diffuse Scattering and Specular Reflection from Facets of Arbitrary Size and Roughness using the Computer Graphics GGX Model

Inspired from the microfacets theory based BRDF models used in computer graphics, the reciprocal, energy conserving Walter et al.'s GGX directional factor is proposed to complement the usual scattering and reflection models for radio propagation. A single formulation of the E field is derived to fit the well-known expressions spanning from the specular reflection from a large smooth surface to the Lambertian scattering from a very rough surface. Near the specular direction, the proposed formulation is similar to the Phong and Degli-Esposti's directional models. This similarity is exploited to propose a simplification of the directional model. The GGX based formulation has two fitting parameters related to the material and the roughness of the facets. Preliminary comparisons with published measurements are encouraging.