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

  • Xavier ChermainEmail author
  • Frédéric Claux
  • Stéphane Mérillou
Original Article


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. (ACM Trans Graph 33(4):116:1–116:9, 2014; ACM Trans Graph 35(4):56:1–56:9, 2016) 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 masking–shadowing 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. (2016). Our results show that we more closely match ground truth renderings than their methods.


Microfacet BRDF Specular normal maps Microstructures Glints 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

Supplementary material 1 (avi 221998 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CNRS, XLIM, UMR 7252Univ. LimogesLimogesFrance

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