The distance sampling is mostly based on weighted delta tracking from
[Monte Carlo Methods for Volumetric Light Transport Simulation]
(http://iliyan.com/publications/VolumeSTAR/VolumeSTAR_EG2018.pdf).
The recursive Monte Carlo estimation of the Radiative Transfer Equation is
\[\langle L \rangle=\frac{\bar T(x\rightarrow y)}{\bar p(x\rightarrow
y)}(L_e+\sigma_s L_s + \sigma_n L).\]
where \(\bar T(x\rightarrow y) = e^{-\bar\sigma\Vert x-y\Vert}\) is the
majorant transmittance between points \(x\) and \(y\), \(p(x\rightarrow
y) = \bar\sigma e^{-\bar\sigma\Vert x-y\Vert}\) is the probability of
sampling point \(y\) from point \(x\) following exponential
distribution.
At each recursive step, we randomly pick one of the two events
proportional to their weights:
* If \(\xi < \frac{\sigma_s}{\sigma_s+\vert\sigma_n\vert}\), we sample
scatter event and evaluate \(L_s\).
* Otherwise, no real collision happens and we continue the recursive
process.
The emission \(L_e\) is evaluated at each step.
This also removes some unused volume settings from the UI:
* "Max Steps" is removed, because the step size is automatically specified
by the volume octree. There is a hard-coded threshold `VOLUME_MAX_STEPS`
to prevent numerical issues.
* "Homogeneous" is automatically detected during density evaluation
An option "Unbiased" is added to the UI. When enabled, densities above
the majorant are clamped.
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