A radiative transfer framework for rendering materials with anisotropic structure
Wenzel Jakob, Adam Arbree, Jon Moon, Kavita Bala, Stephen Marschner
Proceedings of SIGGRAPH 2010 (SIGGRAPH 2010)
Download
(pdf), Expanded tech report
Presentation:
pdf, keynote
Movie
Abstract:
The radiative transfer framework that underlies all current rendering of
volumes is limited to scattering media whose properties are invariant to
rotation. Many systems allow for "anisotropic scattering," in the sense that
scattered intensity depends on the scattering angle, but the standard equation
assumes that the structure of the medium is isotropic. This limitation impedes
physics-based rendering of volume models of cloth, hair, skin, and other
important volumetric or translucent materials that do have anisotropic
structure. This paper presents an end-to-end formulation of physics-based
volume rendering of anisotropic scattering structures, allowing these materials
to become full participants in global illumination simulations.
We begin with a generalized radiative transfer equation, derived from
scattering by oriented non-spherical particles. Within this framework, we
propose a new volume scattering model analogous to the well-known family of
microfacet surface reflection models; we derive an anisotropic diffusion
approximation, including the weak form required for finite element solution and
a way to compute the diffusion matrix from the parameters of the scattering
model; and we also derive a new anisotropic dipole BSSRDF for anisotropic
translucent materials. We demonstrate results from Monte Carlo, finite element,
and dipole simulations. All these contributions are readily implemented in
existing rendering systems for volumes and translucent materials, and they all
reduce to the standard practice in the isotropic case.