<p>The goal of Heitz et al.'s model is pretty much the opposite of subsurface scattering: They only consider surface scattering, i.e. the ray can never enter the material.</p>

<p>Because microfacets are statistical in nature, they can recast their problem in such a way that it can be solved by microflakes, which allows them to compute properties such as the mean free path to derive a heightfield sampling procedure. However, even though they use microflake theory, they still solve the same problem of multiple scattering on microfacets, and their result is still a BSDF, not a subsurface scattering model.</p>

<p>Because it is a BSDF, the path exits at the same location as it hit the surface. This is also mentioned in the introduction:</p>

<blockquote>
  <p>Note that our volume-scattering process models the interaction with a surface, but its application in rendering is virtual in that no displacements occur, i.e. the incident and exitant location are the same and the resulting plane-parallel radiometry produces a BSDF.</p>
</blockquote>

CC BY-SA 3.0
2015-11-05T01:57:04.717Z
2015-11-05T01:57:04.717Z
Benedikt Bitterli
<p>The <a href="https://eheitzresearch.wordpress.com/240-2/" rel="noreferrer">Multiple Scattering Microfacet BSDFs with the Smith Model</a> paper describes a statistical model for replacing the masking-shadowing functions in microfacet BSDFs (which account for paths with more than one surface intersection by setting their contribution to 0) with a distribution which can be path traced and allows the a ray to intersect a microfacet surface several times before exiting.</p>

<p>They do this by modifying a volumetric (microflake) model to behave like a heightfield: to never collide with anything "above" the surface and to always collide with anything "below" the surface.</p>

<p><a href="https://i.sstatic.net/kTAw4.png" rel="noreferrer"><img src="https://i.sstatic.net/kTAw4.png" alt="Microsurface vs modified microflake volume"></a></p>

<p>The result, using wording from their slides, is that "the ray can never go through the Smith volume; the model creates an opaque surface-like interface."</p>

<p>Is this model compatible with traditional diffuse subsurface scattering, where a path can travel a perceptible (macro-scale) distance through a surface before exiting? Or is this simply a specular BSDF with no intention of modeling long paths internal to a surface, to be combined with a diffuse BSDF that adds that component?</p>

<p>(Does the microflake model of volumetric rendering normally separate diffuse and specular, or is "diffuse" simply a path that bounces around so many times that the outgoing direction is uniformly distributed?)</p>

<brdf><scattering><subsurface-scattering><microfacet>
How does Smith multiple scattering interact with diffuse subsurface scattering?
John Calsbeek
# How does Smith multiple scattering interact with diffuse subsurface scattering?

(Asked by: username_0 on 2015-11-04)

The [Multiple Scattering Microfacet BSDFs with the Smith Model](https://eheitzresearch.wordpress.com/240-2/) paper describes a statistical model for replacing the masking-shadowing functions in microfacet BSDFs (which account for paths with more than one surface intersection by setting their contribution to 0) with a distribution which can be path traced and allows the a ray to intersect a microfacet surface several times before exiting.

They do this by modifying a volumetric (microflake) model to behave like a heightfield: to never collide with anything "above" the surface and to always collide with anything "below" the surface.

[![Microsurface vs modified microflake volume](https://i.sstatic.net/kTAw4.png)](https://i.sstatic.net/kTAw4.png)

The result, using wording from their slides, is that "the ray can never go through the Smith volume; the model creates an opaque surface-like interface."

Is this model compatible with traditional diffuse subsurface scattering, where a path can travel a perceptible (macro-scale) distance through a surface before exiting? Or is this simply a specular BSDF with no intention of modeling long paths internal to a surface, to be combined with a diffuse BSDF that adds that component?

(Does the microflake model of volumetric rendering normally separate diffuse and specular, or is "diffuse" simply a path that bounces around so many times that the outgoing direction is uniformly distributed?)

**Tags:** brdf, scattering, subsurface-scattering, microfacet


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## 1 answers

### Answer by username_1 on 2015-11-05. Score: 8 | Accepted answer

The goal of Heitz et al.'s model is pretty much the opposite of subsurface scattering: They only consider surface scattering, i.e. the ray can never enter the material.

Because microfacets are statistical in nature, they can recast their problem in such a way that it can be solved by microflakes, which allows them to compute properties such as the mean free path to derive a heightfield sampling procedure. However, even though they use microflake theory, they still solve the same problem of multiple scattering on microfacets, and their result is still a BSDF, not a subsurface scattering model.

Because it is a BSDF, the path exits at the same location as it hit the surface. This is also mentioned in the introduction:

> Note that our volume-scattering process models the interaction with a surface, but its application in rendering is virtual in that no displacements occur, i.e. the incident and exitant location are the same and the resulting plane-parallel radiometry produces a BSDF.


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