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Merged
AdrienHerubel merged 4 commits into from
Jan 20, 2026
+14 −54
Merged

transmission_scatter sets volume albedo directly #286

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2db0b82
transmission_scatter sets volume albedo directly
portsmouth Dec 8, 2025
45aafd2
clarify wording
portsmouth Dec 9, 2025
8f6fc7b
Merge branch 'dev_1.2' into transmission_scatter_improvements
jstone-lucasfilm Dec 9, 2025
249d8b9
Merge branch 'dev_1.2' into transmission_scatter_improvements
portsmouth Jan 20, 2026
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23 changes: 8 additions & 15 deletions index.html
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Expand Up @@ -819,27 +819,20 @@
The volumetric properties of $V^\infty_\mathrm{dielectric}$ are specified as follows.
The RGB **`transmission_color`** $\mathbf{T}$ and scalar **`transmission_depth`** $\lambda$ parameter pair is a commonly used artist-friendly way to set the volumetric medium extinction coefficient $\boldsymbol{\mu}_t$.

The **`transmission_depth`** is the distance traveled inside the medium by white light before its color becomes exactly **`transmission_color`** by Beer's law, determining the extinction coefficient of the interior medium $\boldsymbol{\mu}_t$ as follows:
The **`transmission_depth`** is the distance traveled inside the medium by white light before its color becomes exactly **`transmission_color`** by Beer's law (assuming homogeneity), determining the extinction coefficient of the interior medium $\boldsymbol{\mu}_t$ as follows:
\begin{equation}
\boldsymbol{\mu}_t = - \frac{\ln \mathbf{T}} {\lambda} \ .
\end{equation}
Being a length, **`transmission_depth`** can be any value greater than or equal to zero. For convenience, we make the soft range $[0, 1]$, thus covering common cases. However when **`transmission_depth`** $\lambda$ is zero, it is assumed that the interior medium is absent ($\boldsymbol{\mu}_t=0$) and **`transmission_color`** is used instead to non-physically tint the dielectric refraction Fresnel factor multiplicatively by a constant amount (ignoring the dielectric energy balance).

The **`transmission_scatter`** parameter $\mathbf{S}$ directly sets the medium scattering coefficient $\boldsymbol{\mu}_s$ (as a multiple of the inverse **`transmission_depth`**):
The **`transmission_scatter`** parameter $\mathbf{\Omega}_s$ specifies the single-scattering albedo of the medium, which thus by definition specifies the scattering coefficient $\boldsymbol{\mu}_s$ in terms of the extinction coefficient $\boldsymbol{\mu}_t$ as:
\begin{equation}
\boldsymbol{\mu}_s = \frac{\mathbf{S}} {\lambda} \ .
\boldsymbol{\mu}_s = \mathbf{\Omega}_s \, \boldsymbol{\mu}_t \ .
\end{equation}
The **`transmission_scatter`** color thus controls the observed color of the single-scattered light. (Note that in the case **`transmission_depth`** $\lambda$ is zero, however, the scattering coefficient is ignored). The absorption coefficient $\boldsymbol{\mu}_a$ is then computed as
\begin{equation}
\boldsymbol{\mu}_a = \boldsymbol{\mu}_t - \boldsymbol{\mu}_s \ .
\end{equation}
If any component of $\boldsymbol{\mu}_a$ is negative, then $\boldsymbol{\mu}_a$ is shifted by enough gray to make all the components positive, i.e.: [^component_wise]
\begin{eqnarray}
&& \mathrm{if \;\; min(\boldsymbol{\mu}_a)} < 0 \nonumber \\
&& \quad\quad \boldsymbol{\mu}_a \leftarrow \boldsymbol{\mu}_a - \mathrm{min}(\boldsymbol{\mu}_a) \ .
\end{eqnarray}
After this shifting, the final extinction coefficient is given by the new $\boldsymbol{\mu}_a + \boldsymbol{\mu}_s$.
This formulation produces volumetric parameters which reproduce reasonably well the independently specified colors of the transmitted and single-scattered light. Finally the medium phase function anisotropy $g \in [-1, 1]$ is given by **`transmission_scatter_anisotropy`** (the standard Henyey--Greenstein phase function is assumed [^anisotropy_g]).
The **`transmission_scatter`** color thus controls the observed color of the single-scattered light.
Single-scattering is expected to be most dominant in the types of thin, highly-absorbing media that this volume is used for, thus this formulation produces volumetric parameters which reproduce reasonably well the independently specified colors of the transmitted and single-scattered light.

Finally the medium phase function anisotropy $g \in [-1, 1]$ is given by **`transmission_scatter_anisotropy`** (the standard Henyey--Greenstein phase function is assumed [^anisotropy_g]).

![](images/transmission1.jpg width=99%) ![](images/transmission2.jpg width=99%) ![](images/transmission3.jpg width=99%)
<div class="shifted-caption">
Expand Down Expand Up @@ -881,7 +874,7 @@
**`transmission_weight`** | Weight | `float` | $ [0, 1] $ | | $ 0 $ | Mix weight between translucent base and opaque base slabs
**`transmission_color`** | Color | `color3` | $ [0, 1]^3 $ | | $ (1, 1, 1) $ | Transmission color, specifies the extinction of $V^\infty_\mathrm{dielectric}$
**`transmission_depth`** | Depth | `float` | $ [0, \infty) $ | $ [0, 1] $ | $ 0 $ | Controls the depth into the volume at which the **`transmission_color`** is realized; if zero, acts as a constant (on-surface) transmission tint
**`transmission_scatter`** | Scatter | `color3` | $ [0, 1]^3 $ | | $ (0, 0, 0) $ | Scattering coefficient of the interior medium
**`transmission_scatter`** | Scatter | `color3` | $ [0, 1]^3 $ | | $ (0, 0, 0) $ | Single-scattering albedo of the interior medium $V^\infty_\mathrm{dielectric}$
**`transmission_scatter_anisotropy`** | Anisotropy | `float` | $ [-1, 1] $ | | $ 0 $ | Anisotropy of the Henyey--Greenstein phase function of the interior medium $V^\infty_\mathrm{dielectric}$
**`transmission_dispersion_scale`** | Dispersion scale | `float` | $ [0, 1] $ | | $ 0 $ | Linearly scales the amount of dispersion
**`transmission_dispersion_abbe_number`** | Abbe number | `float` | $ [0, \infty) $ | $ [9, 91] $ | $ 20 $ | Physical Abbe number of the base dielectric medium
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45 changes: 6 additions & 39 deletions reference/open_pbr_surface.mtlx
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Expand Up @@ -379,54 +379,21 @@
<input name="in1" type="vector3" nodename="extinction_coeff_denom" />
<input name="in2" type="vector3" nodename="transmission_depth_vector" />
</divide>
<convert name="transmission_scatter_vector" type="vector3">
<convert name="transmission_scatter_albedo_vector" type="vector3">
<input name="in" type="color3" nodename="transmission_scatter_clamped" />
</convert>
<divide name="scattering_coeff" type="vector3">
<input name="in1" type="vector3" nodename="transmission_scatter_vector" />
<input name="in2" type="vector3" nodename="transmission_depth_vector" />
</divide>
<multiply name="scattering_coeff" type="vector3">
<input name="in1" type="vector3" nodename="transmission_scatter_albedo_vector" />
<input name="in2" type="vector3" nodename="extinction_coeff" />
</multiply>
<subtract name="absorption_coeff" type="vector3">
<input name="in1" type="vector3" nodename="extinction_coeff" />
<input name="in2" type="vector3" nodename="scattering_coeff" />
</subtract>
<extract name="absorption_coeff_x" type="float">
<input name="in" type="vector3" nodename="absorption_coeff" />
<input name="index" type="integer" value="0" />
</extract>
<extract name="absorption_coeff_y" type="float">
<input name="in" type="vector3" nodename="absorption_coeff" />
<input name="index" type="integer" value="1" />
</extract>
<extract name="absorption_coeff_z" type="float">
<input name="in" type="vector3" nodename="absorption_coeff" />
<input name="index" type="integer" value="2" />
</extract>
<min name="absorption_coeff_min_x_y" type="float">
<input name="in1" type="float" nodename="absorption_coeff_x" />
<input name="in2" type="float" nodename="absorption_coeff_y" />
</min>
<min name="absorption_coeff_min" type="float">
<input name="in1" type="float" nodename="absorption_coeff_min_x_y" />
<input name="in2" type="float" nodename="absorption_coeff_z" />
</min>
<convert name="absorption_coeff_min_vector" type="vector3">
<input name="in" type="float" nodename="absorption_coeff_min" />
</convert>
<subtract name="absorption_coeff_shifted" type="vector3">
<input name="in1" type="vector3" nodename="absorption_coeff" />
<input name="in2" type="vector3" nodename="absorption_coeff_min_vector" />
</subtract>
<ifgreater name="if_absorption_coeff_shifted" type="vector3">
<input name="value1" type="float" value="0.0" />
<input name="value2" type="float" nodename="absorption_coeff_min" />
<input name="in1" type="vector3" nodename="absorption_coeff_shifted" />
<input name="in2" type="vector3" nodename="absorption_coeff" />
</ifgreater>
<ifgreater name="if_volume_absorption" type="vector3">
<input name="value1" type="float" nodename="transmission_depth_nonnegative" />
<input name="value2" type="float" value="0.0" />
<input name="in1" type="vector3" nodename="if_absorption_coeff_shifted" />
<input name="in1" type="vector3" nodename="absorption_coeff" />
<input name="in2" type="vector3" value="0.0,0.0,0.0" />
</ifgreater>
<ifgreater name="if_volume_scattering" type="vector3">
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