Subsurface light scattering describes how light bounces around inside of translucent materials and is emitted from a different location on the object. This is often seen in marble, milk, and skin. Subsurface light scattering is necessary in computer graphics in order to realistically render many translucent objects.

Scattering equations were first used in graphics in the one dimensional case. Max et. al used the equations to compute light scattering in tree canopies. His scattering function was represented by a system of ordinary differential equations which he solved with Runge-Kutta [1].

In the three dimensional case when computing light scattering using the incident and emitted light rays, the function can be 10 dimensions to specify the two rays. To deal with the 3 dimensional case a more general solution technique is often used, Monte Carlo integration. Monte Carlo integration is ideal for high dimensional integration where other methods fail with discontinuous, high dimension, and complex models.

The Monte Carlo method works by randomly sampling the domain of incident and emitted light rays. While there are too many light rays to calculate all of the light transported, the randomized selection starts at the outside layer of the model and works its way into the model sampling how light is transmitted according to the scattering equations. The initial incident ray is scattered into multiple other rays which the Monte Carlo method follows and calculates deeper into the model. In this recursive way, the Monte Carlo method uniformly samples the light transmitted and creates a good approximation for the subsurface light scattering. [2]

Subsurface light scattering for skim, whole, and diffuse milk. [3]

As we can see, the ODE solver Runge-Kutta and Monte Carlo methods, both of which are important numerical methods in scientific computing, are integral to subsurface light scattering simulation.

[1] Nelson Max, Curtis Mobley, Brett Keating, and En-Hua Wu, Plane-parallel radiance transport for global illumination in vegetation, Eurographics Rendering Workshop 1997, Eurographics, Springer Wien, June 1997, pp. 239.250.

[2] Pharr, M. and Hanrahan, P. 2000. Monte Carlo evaluation of non-linear scattering equations for subsurface reflection. In Proceedings of the 27th Annual Conference on Computer Graphics and interactive Techniques International Conference on Computer Graphics and Interactive Techniques. ACM Press/Addison-Wesley Publishing Co., New York, NY, 75-84

[3] Jensen, H. W., Marschner, S. R., Levoy, M., and Hanrahan, P. 2001. A practical model for subsurface light transport. In Proceedings of the 28th Annual Conference on Computer Graphics and interactive Techniques SIGGRAPH ‘01. ACM, New York, NY, 511-518.