“Unbiased VNDF Sampling for Backfacing Shading Normals” by Tokuyoshi

  • ©Yusuke Tokuyoshi



Entry Number: 29


    Unbiased VNDF Sampling for Backfacing Shading Normals



    Shading normals are widely used in computer graphics productions (e.g., movies and video games) to improve the visual appearance without increasing the complexity of geometry. However, the differ- ence between shading normals and geometry normals can violatephysically based assumptions used in rendering techniques. One problem caused by this violation is that a bias can be produced in importance sampling according to a visible normal distribution function (VNDF) [Heitz and d’Eon 2014] when a shading normal is backfacing to an incident direction. This is because a masking function is directly used as the normalization factor of the VNDF, while most masking functions are modeled assuming a geometry normal. In this talk, we present a corrected normalization factor to avoid the bias in VNDF sampling for the Smith [1967] and V-cavity [Cook and Torrance 1982] masking models. Our key insight is that in these models microfacets can be assumed to be single sided and partially visible from below the horizon (Fig. 2). Using our normalization factor derived from this single-sided assumption, we are able to perform unbiased VNDF sampling for backfacing shading normals. Our correction is easy to implement and has a negligible impact on performance especially for the Smith model.


    Robert L. Cook and Kenneth E. Torrance. 1982. A Reflectance Model for Computer Graphics. ACM Trans. Graph. 1, 1 (1982), 7–24. Eric Heitz. 2014. Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs. J. Comput. Graph. Tech. 3, 2 (2014), 48–107. Eric Heitz. 2018. Sampling the GGX Distribution of Visible Normals. J. Comput. Graph. Tech. 7, 4 (2018), 1–13.

    Eric Heitz and Eugene d’Eon. 2014. Importance Sampling Microfacet-Based BSDFs Using the Distribution of Visible Normals. Comput. Graph. Forum 33, 4 (2014), 103–112. Wenzel Jakob. 2014. An Improved Visible Normal Sampling Routine for the Beckmann Distribution. Technical Report. ETH Zürich.

    Bruce G. Smith. 1967. Geometrical shadowing of a random rough surface. IEEE Trans. Antennas Propag. 15, 5 (1967), 668–671.

    Bruce Walter, Stephen R. Marschner, Hongsong Li, and Kenneth E. Torrance. 2007. Microfacet Models for Refraction Through Rough Surfaces. In EGSR ’07. 195–206.


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