3D geometric attenuation factor for discrete Gaussian microsurfaces

The geometric attenuation factor plays an important role in the construction of polarized bidirectional reflection distribution function (pBRDF) model, but the traditional geometric attenuation factor theory neglects the influence of microsurface height on the shadowing and masking effects of light. Therefore, we present a geometric attenuation factor related to the height of the discrete Gaussian microsurface based on microfacet theory. We correspond each sampled point on the microsurface to an element in the attenuation matrix, and assign values to the elements of the attenuation matrix by determining whether the sampling points are illuminated or observable. Finally, we can get the numerical solution of the geometric attenuation factor of the 3D discrete Gaussian microsurface by calculating the attenuation matrix. The results show that the presented geometric attenuation factor is reasonable and effective, and can be better applied to pBRDF model to improve the accuracy of pBRDF model.