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

Draft

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

• 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.

• Overview
• Extending Materials
• Properties
• Scattering
  • Attenuation
  • Single-Scatter Albedo
  • Multi-Scatter Albedo
  • Phase Function
• Scattering & (Diffuse-)Transmission
• Schema
• References
• Appendix: Full Khronos Copyright Statement

KHR_materials_volume defines surfaces as interfaces between volumes and provides tools for specifying attenuation via absorption in homogeneous volumes, but it lacks a definition for scattering. Scattering refers to the wavelength-dependent redirection of light upon particle interaction, while absorption is the wavelength-dependent reduction of light energy along a path. This extension builds on the definitions in KHR_materials_volume.

The scattering properties are defined by adding the KHR_materials_volume_scatter extension to any glTF material that also uses KHR_materials_volume.

"materials": [
    {
        "extensions": {
            "KHR_materials_volume_scatter": {
                "multiscatterColor": [ 0.572, 0.227, 0.075 ],
                "scatterAnisotropy": 0.3
            },
            "KHR_materials_volume": {
                "attenuationColor": [0.9, 0.9, 0.9],
                "attenuationDistance": 0.01
            },
            "KHR_materials_diffuse_transmission": {
                "diffuseTransmissionFactor": 1.0,
            }
        }
    }
]

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

KHR_materials_volume defines the attenuation coefficient as a sum of absorption and scattering coefficients: $\sigma_t = \sigma_a + \sigma_s.$ It further notes that attenuation from scattering events is ignored by assuming $\sigma_s$ to be zero. Combining KHR_materials_volume_scatter with KHR_materials_volume lifts this restriction on the scattering part.

The two derived parameters attenuation color $c$ and attenuation distance $d$ that relate to the attenuation coefficient as

$$ \sigma_t = \frac{-log(c)}{d} $$

now not only consider absorption but also scattering events. The same applies to the definition of the volume transmittance

$$ T(x) = e^{-\sigma_t x}. $$

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

Where the parameterization of KHR_materials_volume provides control on the density of a medium that absorbs and scatters, KHR_materials_volume_scatter provides control on just the scattering part of the medium interaction.

The ratio of scattering to total attenuation is given as single-scatter albedo $\rho_{ss}$

$$ \rho_{ss} = \frac{\sigma_s}{\sigma_t}. $$

Rendering algorithms that implement volumetric scattering are usually interested in the scattering coefficient. Given $\rho_{ss}$ and $\sigma_t$ the scattering coefficient is

$$ \sigma_s = \sigma_t \rho_{ss} = \sigma_t - \sigma_a, $$

and for completeness, the absorption coefficient:

$$ \sigma_a = \sigma_t (1 - \rho_{ss}). $$

The single-scatter albedo could be used to parameterize scattering directly, but it has its drawbacks. 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) use an alternative, more intuitive term, the multi-scatter albedo $\rho_{ms}$. Assuming commonly used values for scatter distances, it is a good approximation to the perceived color of an object after many bounces. $\rho_{ss}$ can be calculated from $\rho_{ms}$ as follows

$$ \rho_{ss} = 1 - (4.09712 + 4.20863 \rho_{ms} - \sqrt{9.59217 + 41.6808 \rho_{ms} + 17.7126 \rho_{ms}^2})^2 $$

For a single scattering event, the phase function $p(\mathbf{v},\mathbf{l})$ determines the probability density of outgoing directions $\mathbf{l}$ given an incident direction $\mathbf{v}$ at a scattering event. We use the phase function developed by Henyey-Greenstein. It is controlled by a single parameter g in the range [−1,1], the scatterAnisotropy parameter.

$$ p(\mathbf{v},\mathbf{l}; g) = \frac{1}{4 \pi} \frac{1-g^2}{(1+g^2+2g(\mathbf{v} \cdot \mathbf{l}))^{3/2}} $$

For any pair of incident and outgoing directions $\mathbf{v}$ and $\mathbf{l}$.

g = -0.95	g = 0.0	g = 0.95
Top-lit, dense scattering medium for different scatter anisotropy values.

For dense subsurface scattering materials like skin or wax (where the scattering coefficient $\sigma_s$​ is high), it is recommended to use KHR_materials_diffuse_transmission over KHR_materials_transmission. In such cases, the visual difference between diffuse and regular transmission is minimal, as volume scattering primarily determines the appearance, with boundary interactions having a small effect.

Using diffuse transmission signals the renderer that the material is dense, eliminating the need to analyze geometry and scattering distance. For instance, a small object with low scattering might appear transparent, but a larger one would appear denser at the same scattering coefficient. Diffuse transmission also enables a translucent look regardless of object size.

This cue allows renderers to use diffusion approximation rather than random walk subsurface scattering, producing near-ground-truth results for dense materials with greater efficiency, essential for both real-time and offline rendering. Christensen and Burley (2015) demonstrate the mapping of physical parameters to diffusion-based reflectance profiles, while Jimenez et al. (2015) introduce a real-time method using a separable kernel for reflectance profile rendering.

• glTF.KHR_materials_subsurface.schema.json

• Christensen, P. and B. Burley (2015): Approximate Reflectance Profiles for Efficient Subsurface Scattering
• Louis G. Henyey and Jesse L. Greenstein: Diffuse radiation in the galaxy. Astrophysical Journal 93, 70–83, 1941.
• Jimenez J., K. Zsolnai, A. Jarabo, C. Freude, T. Auzinger, X.-C. Wu, J. Pahlen, M. Wimmer and D. Gutierrez (2015): Separable Subsurface Scattering
• Kulla C., Conty A. (2017): Revisiting Physically Based Shading at Imageworks

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