Visibility Evaluation in Microfacet Theory

Reflectance models capture many types of visual appearances. The most plausible reflectance models follow the Microfacet theory, which is specifically based on statistical representations, with an analytic visibility term. This visibility term has a significant impact on appearance. Visibility computed with the masking term proposed by Smith (1967), and revisited by Ashikhmin et al. (2000), is nowadays considered as the most plausible in the literature. It is simple and efficient to evaluate for statistical distributions, but it relies on assumptions that are not necessarily respected by real surfaces. This article proposes an in-depth study of masking for meshed height-field surfaces, generated either from measured real-world materials or from functions derived from distributions of surface normals. We experimentally estimate the masking (and shadowing) of surfaces using a ray-casting technique, and compare their measurements with the theoretical model from Smith and Ashikhmin et al. We show that their assumptions are too restrictive for a majority of real-world surfaces. We propose a model capable of predicting how close the theoretical masking term can be from the masking term estimated by a ray-casting approach. Although most surfaces break their assumptions, our results show that the term from Smith and Ashikhmin et al. can still be reasonably employed for a fraction in a set of more than 400 measured surfaces, with low errors compared to a ray-casting masking estimation, much lower computation times, and very similar visual appearances. Our model can be used to predict the incurred error on a physically-based rendering simulation with a microfacet-based BRDF created from real-world surfaces, instead of explicitly calculating the masking term from its height field.