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KHR_materials_sss

Contributors

  • TODO: Name, affiliation, and contact info for each contributor

Status

Draft

Dependencies

Written against the glTF 2.0 spec. Needs to be combined with KHR_materials_volume

Exclusions

  • This extension must not be used on a material that also uses KHR_materials_pbrSpecularGlossiness.
  • This extension must not be used on a material that also uses KHR_materials_unlit.

Table of Contents

Overview

KHR_materials_volume explains how we turn surfaces into interfaces between volumes. It also gives us the necessary tools to define the effect of absorption inside homogeneous volumes. What it lacks, is the definition of scattering. Scattering is the wavelength-dependent change of direction which occurs when light interacts with particles. Whereas absorption is the wavelength-dependent reduction of light energy along a path. This extension can be considered as an augmentation of the definitions given in KHR_materials_volume.

Interaction of light rays inside the volume and at the boundaries. The volume is homogeneous and has an index of refraction of 1.5.

Extending Materials

TODO: Clarify location of scattering extensions. volume or material The scattering properties are defined by adding the KHR_materials_sss extension to any glTF material.

materials: [
    {
        "extensions": {
            "KHR_materials_sss": {
                "scatterDistance": 0.01,
                "scatterColor": [ 0.572, 0.227, 0.075 ]
            }
        }
    }
]

Properties

The extension defines the following parameters to describe the scattering behavior.

Type Description Required
scatterDistance number Average distance in meters that light travels in the medium before it collides with a particle and scatters No, default: +Infinity
scatterColor number[3] Color as a result of scatter events No, default: [0, 0, 0]

Scattering

In rendering literature, the scattering behavior is most commonly described by the scattering coefficient σs. The scattering coefficient is a probability density with the unit 1/m2 and values in the range [0, inf]. The sum of absorption and scattering coefficients is referred to as the attenuation (or extinction) coefficient

σt = σa + σs

Analogous to the parameterization of the absorption coefficient in KHR_materials_volume, this extension parameterizes the scattering coefficient in terms of scattering color cs and scattering distance ds.

σs = -log(cs) / ds

The definition of the scattering coefficient σs replaces the zero constant in KHR_materials_volume. As the volume extension already uses the notation of attenuation coefficient σt, the derivation of the transmittance function is unchanged

T(x) = e-σtx

Instead of only taking into account absorption, T now corresponds to a change in radiance along a path as light travels through a medium with absorbing and scattering particles.

A simple, diffuse-only material (left) and a material that makes use of subsurface scattering (right). The base color of the diffuse material is set to the same color as the subsurface color of the subsurface scattering material. Due to the albedo mapping the final color of the object is very similar.

Phase Function

The phase function p used for scattering inside the medium is isotropic. For any pair of incident and outgoing directions k1 and k2, p(k1, k2) = 1 / (4π).

Scattering, Translucency & Transmission

For best results, we recommend using KHR_materials_translucency instead of KHR_materials_transmission in case the medium exhibits strong subsurface scattering (large values for the scattering coefficient σs). Examples for these dense materials are skin or candle wax. The visual difference between translucency and transmission is small in this case, as the path a light travels is dominated by volume scattering. The scattering interaction at the volume boundary has only a small effect on the final result.

The benefit of using translucency is that it signals the renderer that a material is dense, without the need to analyze geometry and scattering distance. Typically, the size of the volume in relation to the scattering coefficient determines the density of the object. A tiny object with low scattering coefficient may appear transparent, but increasing the size of the object will make it appear denser, although the scattering coefficient stays the same. If translucency is being used instead of highly glossy transmission, the material appears to be translucent independent of its size.

Consequently, renderers may use translucency as a cue to switch to diffusion approximation instead of random walk subsurface scattering. Diffusion approximation gives results that are very close to ground-truth for dense materials, but can be much faster. This is crucial for real-time implementations (which cannot do random walk), but also beneficial for offline rendering. Christensen and Burley (2015) show how to map the physical parameters for attenuation and subsurface scattering to an appropriate reflectance profile for diffusion approximation and compare results between approximation and ground-truth random walk. Jimenez et al. (2015) present a method to render reflectance profiles in real-time by approximating the profile with a separable kernel.

Comparison of combining subsurface scattering with either transmission or translucency. Left: Rough transmission and subsurface scattering. Middle: Translucency and subsurface scattering. Right: Translucency without subsurface scattering using a thin-walled material. Colors are adjusted manually so that they look similar in the three configurations. This adjustment is needed in order to account for differences in distances and to minimize the impact of energy loss from the rough microfacet BTDF.

Alternative Parameterization

An alternative parameterization for scattering uses the scatter radius (or mean-free path) and the single-scatter albedo ρss.

The mean-free path is defined as

mfp = 1.0 / σt

It can be interpreted as the average distance that a photon travels in a medium before interacting with a particle for scattering or absorption.

The single-scatter albedo is the color of a single scattering interaction in the medium. Light that is scattered by a particle will be tinted with this color. An albedo of 0 (black) disables scattering, resulting in a medium that only absorbs.

ρss = σs / σt

With σt and ρss at hand, modified absorption and scattering coefficients can be calculated, which then can can be used to derive the transmission function as defined above.

σa = σt (1 - ρss)

σs = σt ρss = σt - σa

In reality, light scatters multiple times in the medium until it leaves the volume. Depending on the number of bounces, the overall perceived color of the medium differs drastically from what is given by the single-scatter albedo. Kulla and Conty (2017) introduced an alternative, more intuitive term, the multi-scatter albedo ρms. Assuming commonly used values for scatter distances, it is a good approximation to the perceived color of an object after many bounces. ρss can be calculated from ρms as follows

ρss = 1 - (4.09712 + 4.20863 ρms - sqrt(9.59217 + 41.6808 ρms + 17.7126 ρms2))2

TODO: (This section needs more motivation. Why is it there? What's the advantage of the alternative parameterization? We should connect this somehow to the typical BSSRDF implementations that use the attenuation cofficient to "blur" the reflectance profile and subsurface color to weight the blurred result.)

Schema

References

Appendix: Full Khronos Copyright Statement

Copyright 2018-2020 The Khronos Group Inc.

Some parts of this Specification are purely informative and do not define requirements necessary for compliance and so are outside the Scope of this Specification. These parts of the Specification are marked as being non-normative, or identified as Implementation Notes.

Where this Specification includes normative references to external documents, only the specifically identified sections and functionality of those external documents are in Scope. Requirements defined by external documents not created by Khronos may contain contributions from non-members of Khronos not covered by the Khronos Intellectual Property Rights Policy.

This specification is protected by copyright laws and contains material proprietary to Khronos. Except as described by these terms, it or any components may not be reproduced, republished, distributed, transmitted, displayed, broadcast or otherwise exploited in any manner without the express prior written permission of Khronos.

This specification has been created under the Khronos Intellectual Property Rights Policy, which is Attachment A of the Khronos Group Membership Agreement available at www.khronos.org/files/member_agreement.pdf. Khronos grants a conditional copyright license to use and reproduce the unmodified specification for any purpose, without fee or royalty, EXCEPT no licenses to any patent, trademark or other intellectual property rights are granted under these terms. Parties desiring to implement the specification and make use of Khronos trademarks in relation to that implementation, and receive reciprocal patent license protection under the Khronos IP Policy must become Adopters and confirm the implementation as conformant under the process defined by Khronos for this specification; see https://www.khronos.org/adopters.

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