Taming the Shadow TerminatorMatt Jen-Yuan Chiang

Walt Disney Animation StudiosYining Karl Li

Walt Disney Animation StudiosBrent Burley

Walt Disney Animation Studios

(a) Only Shading Normals (b) Estevez et al. [2019] (c) Ours

Figure 1: (a) the shadow terminator appears harshwhen using shading normals. (b) Estevez et al. [2019] softens the terminator but still appearssomewhat harsh. (c) Our modified shadowing function fully softens the terminator without otherwise compromising the look.

ABSTRACTA longstanding problem with the use of shading normals is thediscontinuity introduced into the cosine falloff where part of thehemisphere around the shading normal falls below the geometricsurface. Our solution is to add a geometrically derived shadowingfunction that adds minimal additional shadowing while fallingsmoothly to zero at the terminator. Our shadowing function issimple, robust, efficient and production proven.

CCS CONCEPTS• Computing methodologies→ Rendering; Ray tracing.

KEYWORDSray tracing, global illumination, shading normals

ACM Reference Format:Matt Jen-Yuan Chiang, Yining Karl Li, and Brent Burley. 2019. Taming theShadow Terminator. In Proceedings of SIGGRAPH ’19 Talks. ACM, New York,NY, USA, 2 pages. https://doi.org/10.1145/3306307.3328172

1 INTRODUCTIONShading normals are a widely used technique in computer graphicsfor simulating the visual appearance of fine detail. Shading normalsare produced by using a bump or normal map to perturb an ex-isting geometric surface normal without changing the underlyinggeometric surface; the shading normal is then used in place of the

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surface normal for shading and lighting calculations. Shading nor-mals are relatively computationally inexpensive and use much lessmemory compared to displacement mapping, but decoupling theshading normal from the geometry can introduce artifacts such as apronounced shadow terminator as shown in Figure 1 and explainedin Figure 2.

The harsh terminator can be distracting and can affect the visualinterpretation of the surface material. To alleviate this problem,artists today typically have to either fall back to displacement oruse larger area lights to soften the shadow. To eliminate the harshterminator, we add an additional shadowing factor that smoothlyfalls off to zero at the geometric terminator while preserving ashape close the original cosine falloff.

Ligh

t Sou

rce

Terminator 0.5 1.0 1.5

0.2

0.4

0.6

0.8

1.0Terminator

Brig

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ss

⟨ωs, ωi⟩

Figure 2: With geometric normals (black), brightness follows asmooth cosine falloff to zero at the shadow terminator. With shad-ing normals (red) bent towards the light, brightness does not reachzero at the shadow terminator, resulting in a hard cutoff.

2 RELATEDWORKTo address energy loss when rendering with shading normals,Schüssler et al. [2017] imagined an additional microfacet at eachshading point perpendicular to the geometric surface, and then ac-counted for inter-reflections between the two facets. Unfortunately,the added multiple scattering significantly alters the overall sur-face appearance and also requires a random walk to evaluate. But

SIGGRAPH ’19 Talks, July 28 - August 01, 2019, Los Angeles, CA, USA Matt Jen-Yuang Chiang, Yining Karl Li, and Brent Burley

without the multiple scattering, the shadowing from the additionalmicrofacet is overly dark as shown in Figure 4.

In recent concurrent work, Estevez et al. [2019] addressed thehard terminator problem with an added GGX shadowing factorwith roughness parameter α estimated from the shading normaldeviation measured from the geometric normal. The resulting func-tion softens the terminator less than our approach as shown inFigures 1 and 4. We contrast this method further in the next sec-tion.

3 APPROACH

Figure 3: Micro-surface profile from Schüssler et al. [2017] (top) vs.ours (bottom). Instead of adding a facet perpendicular to the geo-metric surface (a), we add a facet perpendicular to the primary facet(b). When the incoming light is aligned with the shading normal,their method incurs shadowing (c) whereas ours does not. As thelight moves toward the geometric horizon, both methods graduallyreduce the incident illumination to zero (e) and (f).

Inspired by Schüssler et al. [2017], we propose a modified config-uration, illustrated in Figure 3, where the added facet is oriented tomaintain peak brightness when the light is aligned with the shadingnormal, falling smoothly to zero at the geometric terminator. Theshadowing resulting from the added facet is:

G = min[1,

⟨ωд ,ωi ⟩

⟨ωs ,ωi ⟩⟨ωд ,ωs ⟩

](1)

Importantly, when the light is on the geometric side of the shadingnormal (i.e. when ⟨ωд ,ωi ⟩ > ⟨ωд ,ωs ⟩), then G = 1 and no addi-tional shadowing is incurred. However, if G is simply multipliedinto the BRDF as-is then a C1 discontinuity would be introducedat the point where the light direction reaches and moves beyondthe shading normal. To alleviate the discontinuity, we use Hermiteinterpolation going from a slope of 1 to 0 over the range of G from0 to 1, resulting in our final shadowing factor:

G ′ = −G3 +G2 +G (2)

In Figure 4 we briefly contrast our method with the shadow-ing functions from [Schüssler et al. 2017] and [Estevez et al. 2019].The original bump mapping has a harsh terminator compared tothe version without bump mapping. The shadowing function fromSchüssler et al. adds significant darkening well beyond the termi-nator whereas that of Estevez et al. is still somewhat harsh. Incomparison, our function softens the terminator while retainingthe overall look of the surface away from the terminator.

Though our shadowing function produces results often similarto that of Estevez et al., there are significant differences which we

No bump

Original bump

Schussler et al.

Estevez et al.

Ours

Figure 4: Bump mapped cylinder rendered with various shadowingfunctions. The (thresholded) difference from the original is shownto the right.

Figure 5: Contour plots comparing our shadowing function (left)with the one by Estevez et al. (right). The horizontal axis is the lightangle as measured from the geometric normal. The vertical axis isthe deviation of the shading normal from the geometric normal to-wards the light direction.

illustrate in Figure 5. For an unperturbed shading normal (bottomof contour plot), both functions produce no attenuation. However,when the shading normal is perturbed beyond the light direction(upper left triangle of contour plot) our function adds no attenu-ation whereas theirs adds significant attenuation. Generally, forsmall shading normal deviations (lower right of plot), their functionhas less shadowing, and for large deviations (upper right), theirshas more shadowing, and thus their method generally has highercontrast near the terminator which may explain why our methodappears softer.

4 CONCLUSIONS AND FUTUREWORKWe proposed amethod to create soft bumpmap shadow terminators.Our method is artistically pleasing and produces natural cosine-likefalloff for the terminator while maintain the classic normal/bumpmap look elsewhere. Our method is also efficient to compute andeasy to implement, and has been used successfully in production.In the future we would like to look into how to get a closer matchto displacement mapping.

REFERENCESAlejandro Conty Estevez, Pascal Lecocq, and Clifford Stein. 2019. A Microfacet-Based

Shadowing Function to Solve the Bump Terminator Problem. Ray Tracing Gems(2019), 127.

Vincent Schüssler, Eric Heitz, Johannes Hanika, and Carsten Dachsbacher. 2017.Microfacet-based normal mapping for robust Monte Carlo path tracing. ACMTransactions on Graphics (TOG) 36, 6 (2017), 205.