14 Light Transport II: Volume Rendering

The abstractions for representing participating media that were introduced in Chapter 11 describe how media scatter light but they do not provide the capability of simulating the global effects of light transport in a scene. The situation is similar to that with BSDFs: they describe local effects, but it was necessary to start to introduce integrators in Chapter 13 that accounted for direct lighting and interreflection in order to render images. This chapter does the same for volumetric scattering.

We begin with the introduction of the equation of transfer, which generalizes the light transport equation to describe the equilibrium distribution of radiance in scenes with participating media. Like the transmittance equations in Section 11.2, the equation of transfer has a null-scattering generalization that allows sampling of heterogeneous media for unbiased integration. We will also introduce a path integral formulation of it that generalizes the surface path integral from Section 13.1.4.

Following sections discuss implementations of solutions to the equation of transfer. Section 14.2 introduces two Integrators that use Monte Carlo integration to solve the full equation of transfer, making it possible to render scenes with complex volumetric effects. Section 14.3 then describes the implementation of LayeredBxDF, which solves a 1D specialization of the equation of transfer to model scattering from layered materials at surfaces.