Geometric attenuation factor based on scattering theory from randomly rough surface.

The geometrical attenuation factor (GAF) describes the effect of shadowing and masking on surfaces. The GAF is a crucial factor in achieving a high degree of realism in computer graphics and is important for the evaluation of the accuracy of the bidirectional reflectance distribution function (BRDF). The Smith GAF is a simplified algorithm that is calculated on some assumptions and by using the root mean square. The Sun GAF is a brute-force algorithm that is calculated on the given surface; however, the Sun GAF does not consider the incident wavelength and its interaction with the surface. We propose a GAF algorithm that is designed based on Maxwell's equations and the scattering. We consider the incident wavelength, the shape of the rough surface, and the scattering, and validated on generated Gaussian surfaces. The results demonstrated that, to a large extent, the proposed algorithm eliminated the undesired behavior of the Cook-Torrance BRDF model near the grazing angle.