<p>I think the term for this would be &quot;medium with a varying index of refraction&quot;; the term &quot;anisotropic medium&quot; more typically refers to scattering media where the scattering coefficients depend on the direction of the ray (e.g. microflake models). Anyway, there seem to be a few papers on the topic that I was able to find with a quick web search.</p>
<ul>
<li><p><a href="https://d2f99xq7vri1nk.cloudfront.net/legacy_app_files/pdf/wobble.pdf" rel="nofollow noreferrer">Stam and Languénou, Ray Tracing in Non-Constant Media (1996)</a> - derives a differential equation to bend the ray's path, which can be numerically integrated along it using ray marching</p>
</li>
<li><p><a href="https://imaging.cs.cmu.edu/rrte/" rel="nofollow noreferrer">Pediredla et al, Path Tracing Estimators for Refractive Radiative Transfer (2020)</a> - uses Monte Carlo volumetric path tracing, and extends it to handle varying refractive index, using a gradient descent approach to solve the eikonal equation along sampled path segments</p>
</li>
<li><p><a href="https://res.mdpi.com/d_attachment/applsci/applsci-11-00912/article_deploy/applsci-11-00912-v2.pdf" rel="nofollow noreferrer">Zhang et al, Ray Tracing Method of Gradient Refractive Index Medium Based on Refractive Index Step (2021)</a> - approximates the continuously-varying refractive index as piecewise constant slices and treats the interfaces between slices using the usual Snell's law of refraction. It is adaptive to how rapidly the refractive index is changing, taking longer steps where it is nearly constant and short steps where it is rapidly varying</p>
</li>
</ul>

CC BY-SA 4.0
2021-06-27T21:53:43.420Z
2021-06-27T21:53:43.420Z
Nathan Reed
<p>I wish to determine the path taken by a light ray between two points, <span class="math-container">$a$</span> and <span class="math-container">$b$</span>, through an <em>anisotropic</em> medium. More specifically, this medium has an index of refraction which varies as an exponential function of depth.</p>
<p>I'm not terribly familiar with the methods of raytracing in computer graphics, however I understand that such problems are within the domain of raytracing. Algorithmically, how might such a path be determined (ideally, more efficiently than writing and solving systems of differential equations)?</p>

<raytracing><algorithm>
How is raytracing performed in anisotropic media?
10GeV
# How is raytracing performed in anisotropic media?

(Asked by: username_0 on 2021-06-27)

I wish to determine the path taken by a light ray between two points, $a$ and $b$, through an *anisotropic* medium. More specifically, this medium has an index of refraction which varies as an exponential function of depth.

I'm not terribly familiar with the methods of raytracing in computer graphics, however I understand that such problems are within the domain of raytracing. Algorithmically, how might such a path be determined (ideally, more efficiently than writing and solving systems of differential equations)?

**Tags:** raytracing, algorithm


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## 1 answers

### Answer by username_1 on 2021-06-27. Score: 2 | Accepted answer

I think the term for this would be "medium with a varying index of refraction"; the term "anisotropic medium" more typically refers to scattering media where the scattering coefficients depend on the direction of the ray (e.g. microflake models). Anyway, there seem to be a few papers on the topic that I was able to find with a quick web search.

* [Stam and Languénou, Ray Tracing in Non-Constant Media (1996)](https://d2f99xq7vri1nk.cloudfront.net/legacy_app_files/pdf/wobble.pdf) - derives a differential equation to bend the ray's path, which can be numerically integrated along it using ray marching
* [Pediredla et al, Path Tracing Estimators for Refractive Radiative Transfer (2020)](https://imaging.cs.cmu.edu/rrte/) - uses Monte Carlo volumetric path tracing, and extends it to handle varying refractive index, using a gradient descent approach to solve the eikonal equation along sampled path segments
* [Zhang et al, Ray Tracing Method of Gradient Refractive Index Medium Based on Refractive Index Step (2021)](https://res.mdpi.com/d_attachment/applsci/applsci-11-00912/article_deploy/applsci-11-00912-v2.pdf) - approximates the continuously-varying refractive index as piecewise constant slices and treats the interfaces between slices using the usual Snell's law of refraction. It is adaptive to how rapidly the refractive index is changing, taking longer steps where it is nearly constant and short steps where it is rapidly varying


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