A microfacet-based BRDF for the accurate and efficient rendering of high-definition specular normal maps

Abstract

Complex specular microstructures found in glittery, scratched or brushed metal materials exhibit high frequency variations in reflected light intensity. These variations are important for the human eye and give materials their uniqueness and personality. To model such microsurfaces, high definition normal maps are very effective. The works of Yan et al. [21,22] enable the rendering of such material representations by evaluating a microfacet based BRDF related to a whole ray footprint. Still, in specific configurations and especially at grazing angles, their method does not fully capture the expected material appearance. We propose to build upon their work and tackle the problem of accuracy using a more physically based reflection model. To do so, the normal map is approximated with a mixture of anisotropic, noncentered Beckmann normal distribution functions from which a closed form for the maskingshadowing term can be derived. Based on our formal definition, we provide a fast approximation leading to a performance overhead varying from 5% to 20% compared to the method of Yan et al. [22]. Our results show that we more closely match ground truth renderings than their methods.

Glint Rendering based on a Multiple‐Scattering Patch BRDF

“…Several papers improve the performance of their method by either using 4D NDF mixtures [YHMR16] or spherical harmonics [GGN18]. The work of Chermain et al [CCM18] focuses on rendering quality and proposes footprint-relative normalization factors. The importance sampling procedure is efficient since it uses footprint-based NDFs, however visibility information is not used, causing fireflies and zero-radiance paths.…”

“…In practice, we mollify the Dirac distribution of fm to a NDF with tiny roughness αm [YHJ * 14, YHMR16,CCM18] in order to evaluate f 1 (Equation 7). Note that the energy term of Equation 8 still guarantees energy conservation with a mollified Dirac.…”

“…As our footprint k P is Gaussian, we use a Gaussian weight k j for the BRDF in order to have an analytic weighting of f 1 . The standard deviation of k j is set to σ h = h/ √ 8 log 2 as in the methods of Yan et al and Chermain et al [YHMR16,CCM18] to achieve an equal contribution of two adjacent BRDFs when the evaluation point u is halfway between the two (Figure 6). Substituting the sum expression of f 1 (Equation 16) into the single-scattering patch-BRDF (Equation 14) gives…”

“…The complexity of the material is fully taken into account and its related appearance is meant to be faithfully reproduced. ZK16,WWH18], primitive-based BRDF [RGB16] or normal mapbased glint integrators [YHMR16,CCM18,GGN18]. Each kind of method has associated strengths and weaknesses.…”

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Multiple-scattering glint integratorChermain et al [CCM18] Yan et al[YHMR16]Figure 1: Glittery orb illuminated by an environment map using 1,024 spp. The micro-surface is modeled by a specular normal map with high RMS roughness (σ = 1).

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