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KHR_materials_volume

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_transmission or KHR_materials_translucency.

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

By default, a glTF 2.0 material describes the scattering properties of a surface enclosing an infinitely thin volume. The surface defined by the mesh represents a thin wall. The volume extension makes it possible to turn the surface into an interface between volumes. The mesh to which the material is attached defines the boundaries of an homogeneous medium and therefore must be manifold. Volumes provide effects like refraction, absorption and subsurface scattering.


Renderings of various objects (top) and corresponding top-down slice through the scene (bottom). The solid line represents the mesh. The gray area represents the volume. Thin-walled materials can be applied to open (left) and closed meshes (middle). The dashed line indicates the imaginary bounds of the infinitely thin volume. The volumetric material can only be applied to closed meshes (right), resulting in volumetric effects like refraction.

The volume extension has to be combined with KHR_materials_transmission or KHR_materials_translucency. Light that falls onto the volume boundary may enter the volume, depending on the transmission or translucency of the surface's BSDF. Inside the volume, light might be absorbed or scattered by particles in the medium, and eventually hit some surface from inside the volume. It can be a different surface and will most probably be a different point in space compared to the entrance point. At this exit point, if the material properties allow, light may leave the 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.

When light interacts with the surface, it is reflected or refracted at microfacets, taking the roughness of the material into account. The index of refraction is taken from KHR_materials_ior.

Extending Materials

The volumetric properties are defined by adding the KHR_materials_volume extension to any glTF material. A non-zero thickness switches from thin-walled to volumetric behavior. This requires a manifold/closed mesh. The properties of the medium are not texturable, it is assumed to be homogeneous.

materials: [
    {
        "extensions": {
            "KHR_materials_volume": {
                "thicknessFactor": 1.0,
                "attenuationDistance":  0.006,
                "attenuationColor": [ 0.5, 0.5, 0.5 ],
                "subsurfaceColor": [ 0.572, 0.227, 0.075 ]
            }
        }
    }
]

Properties

The extension defines the following parameters to describe the volume.

Type Description Required
thicknessFactor number The thickness of the volume beneath the surface in meters in the local coordinate system of the node. If the value is 0 the material is thin-walled. Otherwise the material is a volume boundary. The doubleSided property has no effect on volume boundaries. No, default: 0.
thicknessTexture textureInfo A texture that defines the thickness, stored in the G channel. This will be multiplied by thicknessFactor. No
attenuationDistance number Density of the medium given as the average distance in meters that light travels in the medium before interacting with a particle. No, default: +Infinity
attenuationColor number[3] The color that white light turns into due to absorption when reaching the attenuation distance. No, default: [1, 1, 1]
subsurfaceColor number[3] The overall color perceived at the surface due to subsurface scattering. No, default: [0, 0, 0]

Thickness Texture

The thickness of a volume enclosed by the mesh is typically quite difficult to compute at run-time in a rasterizer. Since glTF is primarily used with real-time rasterizers, this extension allows for the thickness of the volume to be explicitly defined, either via a 1-channel texture value or as a constant. However, deriving the thickness along a ray from the actual geometry is the preferred approach. Path-traced renderers as well as more sophisticated raster techniques should ignore the thickness texture. Note that it is still necessary to check the thicknessFactor to determine whether the object is thin-walled or volumetric.

Refraction

Light rays falling through the volume boundary are refracted according to the index of refraction (IOR) given in KHR_materials_ior. The IOR determines the refraction angle. If KHR_materials_ior is not available, the IOR is 1.5.

Transmissive sphere with varying index of refraction. From left to right: 1.1, 1.5, 1.9.

Absorption and Subsurface Scattering

Absorption and subsurface scattering are described by the absorption coefficient σa and the scattering coefficient σs. The coefficients σa and σs are wavelength-dependent values in the range [0, Inf]. Such an infinite range makes them hard to be controlled by users.

To provide convenient parameterization for users this extension provides three parameters: attenuation color a, attenuation distance d and subsurface color ρms (see Properties). We will now describe how to derive the physical parameters for absorption and scattering from the user-friendly parameters.

In a first step, we map from attenuation color and distance to the attenuation coefficient σt.

σt = -log(a) / d

In a homogenous medium, σt is constant, and we can compute the fraction of light (radiance) T(x) transmitted after traveling a distance x via Beer's law:

T(x) = e-σtx

The inverse of attenuation coefficient 1 / σt is the mean free path length which gives the average distance light travels in the medium before interacting with a particle. At such an interaction, light may be absorbed or scattered. In our case, we define σt via color and distance separately, so after traveling a distance x = d, we get the attenuation color a:

T(d) = e(-log(a) / d) * d = a

In the next step, we map from our subsurface color parameter ρms to single-scattering albedo ρss.

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

The single-scattering albedo is the color of a particle 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.

Note that scattering will happen many times in the medium until the light leaves the volume, so the overall color ρms will differ significantly from the albedo of the particles ρss. Via the mapping users can control the albedo of surface, i.e., the color that an object appears to have in the final rendering. The mapping was introduced by Kulla and Conty (2017).

Now that we have computed σt and ρss, we can finally derive σa and σs as follows:

σa = σt (1 - ρss)

σs = σt ρss = σt - σa

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).

Base Color and Absorption

Base color and absorption both have an effect on the final color of a volumetric object, but the behavior is different. Base color changes the color of light at the volume boundary. Absorption occurs while the light is traveling through the volume. Depending on the distance the light travels, more or less of it is absorbed, making the overall color of the object dependent on its shape.

Base color changes the amount of light passing through the volume boundary (left). The overall color of the object is the same everywhere, as if the object is covered with a colored, transparent foil. Absorption changes the amount of light traveling through the volume (right). The overall color depends on the distance the light traveled through it; at small distances (tail of the dragon) less light is absorbed and the color is brighter than at large distances.

Transmission and Translucency

The volume extension needs one of KHR_materials_transmission and KHR_materials_translucency to allow light rays to pass through the surface into the volume. Once the volume is entered however, the simulation of absorption and subsurface scattering inside the medium will be independent of the surface properties.

If the extension is combined with KHR_materials_transmission, the refraction occurs at the microfacets. That means that the thin microfacet BTDF is replaced by a microfacet BTDF that takes refraction into account. The roughness parameter affects both reflection and transmission.

Transmissive sphere with varying roughness. From left to right: 0.0, 0.2, 0.4.

If the extension is combined with KHR_materials_translucency, the translucent BTDF remains unchanged.

Translucent sphere with varying roughness. From left to right: 0.0, 0.2, 0.4.

For best results, we recommend using KHR_materials_translucency instead of KHR_materials_transmission in case the medium exhibits strong subsurface scattering (small scattering distance, high subsurface color). 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 attenuation 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 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.

Implementation

This section is non-normative.

The microfacet BTDF ftransmission defined in KHR_materials_transmission now takes refraction into account. That means that we to use Snell's law to compute the modified half vector:

HTR = -normalize(iori * V + ioro * L)

iori and ioro denote the IOR of the incident and transmitted side of the surface, respectively. V is the vector pointing to the camera, L points to the light. In a path tracer that starts rays at the camera, V corresponds to the incident side of the surface, which is the side of the medium with iori.

Incident and transmitted IOR have to be correctly set by the renderer, depending on whether light enters or leaves the object. An algorithm for tracking the IOR through overlapping objects is described by in Schmidt and Budge (2002).

The microfacet BTDF also makes use of the modified half vector and the indices of refraction.

ftransmission = T * baseColor * (1 - FTR) * (abs(dot(L, HTR)) * abs(dot(V, HTR))) / (abs(dot(L, N)) * abs(dot(V, N))) * (ioro2 * GTR * DTR) / (iori * dot(V, HTR) + ioro * dot(L, HTR))2

where T is the transmission percentage defined by KHR_materials_transmission. The DT<R/sub> and GTR terms are the same as in the specular reflection except using the modified half vector HTR calculated from the refraction direction. See Walter et al. (2007) for details.

The Fresnel term FTR now needs to take internal reflection into account. When using the Schlick approximation, care must be taken to use the angle that is on the dense side of the boundary, i.e., the side with the medium that has a higher IOR. In addition, total internal reflection has to be considered. Therefore, we have three cases:

Light enters medium with higher IOR: ioro ≥ iori.

FTR+ = F0 + (1 - F0) * (1 - abs(dot(V, HTR)))^5

Light enters medium with lower IOR and there is no total internal reflection: ioro < iori and sin2(θo) < 1. The angle at the transmitted side of the boundary (medium with lower IOR) θo is computed from the angle of incidence via sin2(θo) = (iori / ioro)2 (1 - dot(V, HTR)2) and thus cos(θo) = sqrt(1 - sin2(θo)).

FTR- = F0 + (1 - F0) * (1 - abs(cos(θo)))^5

Light enters medium with lower IOR and there is total internal reflection: ioro < iori and sin2(θo) ≥ 1.

FTRTIR = 1

Interaction with other extensions

If KHR_materials_specular is used in combination with KHR_materials_volume, specular color and specular modify F0 and F90 of the Fresnel as usual, but with one exception: In case of total internal reflection, F90 is not scaled by the specular parameter of KHR_materials_specular. This allows users to change the specular component of a refractive object without introducing artifacts, i.e., dark appearance in areas where total internal reflection occurs.

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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