Microfacet distributions are considered nowadays as a reference for physically plausible BSDF representations. Many authors have focused on their physical and mathematical correctness, while introducing means to enlarge the range of possible appearances. This article is dedicated to Normal Distribution Functions (NDFs) and the influence of their shape on the rendered material aspect. We provide a complete framework for studying the impact of NDFs on the observed Bidirectional Scattering Distribution Functions (BSDFs). To explore very general NDFs, manually controlled by the user, and including anisotropic materials, we propose to use a piecewise continuous representation. It is derived with its associated Smith shadowing-masking function and importance sampling formulations for ensuring efficient global illumination computations. A new procedure is also proposed in this article for generating an explicit geometric micro-surface, used to evaluate the validity of analytic models and multiple scattering effects. The results are produced with a computer-generated process using path tracing. They show that this generation procedure is suitable with any NDF model, independently from its shape complexity.

Specular microfacet distributions have been successfully employed by many authors for representing glossiness of materials. They are generally combined with a Lambertian term to account for the colored aspect. These representations make use of the Fresnel reflectance factor at the interface, but the transmission factor at the interface should also be managed. One solution is to employ a multi-layered model with a single layer for the rough interface, which requires a numerical simulation for handling the multiple reflections of light between the substrate and the interface. In this paper, we propose rather to use a representation corresponding to a Fresnel interface lying on a Lambertian substrate, for which the multiple reflections of light between the interface and the substrate can be expressed analytically. With this interfaced Lambertian model, we show how Fresnel transmission affects the material appearance for flat and rough surfaces with isotropic and anisotropic distributions, that produce light backscattering effects. We also propose a methodology for using such materials in any physically based Monte Carlo rendering system, as well as an approximate representation, suitable for GPU applications or measured data fitting. Our approach generalizes several previous models, including flat Lambertian materials as well as specular and Lambertian microfacets. Our results illustrate the wide range of materials that can be rendered with this representation.

This paper focuses on microfacet reflectance models, and more precisely on the definition of a new and more general distribution function, which includes both Beckmann's and GGX distributions widely used in the computer graphics community. Therefore, our model makes use of an additional parameter γ, which controls the distribution function slope and tail height. It actually corresponds to a bivariate Student's t-distribution in slopes space and it is presented with the associated analytical formulation of the geometric attenuation factor derived from Smith representation. We also provide the analytical derivations for importance sampling isotropic and anisotropic materials. As shown in the results, this new representation offers a finer control of a wide range of materials, while extending the capabilities of fitting parameters with captured data.