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.

Hair models for computer graphics consist of many curves representing individual hair fibers. In current practice these curves are generated by ad hoc random processes, and in close-up views their arrangement appears plainly different from real hair. To begin improving this situation, this paper presents a new method for measuring the detailed arrangement of fibers in a hair assembly. Many macrophotographs with shallow depth of field are taken of a sample of hair, sweeping the plane of focus through the hair's volume. The shallow depth of field helps isolate the fibers and reduces occlusion. Several sweeps are performed with the hair at different orientations, resulting in multiple observations of most of the clearly visible fibers. The images are filtered to detect the fibers, and the resulting feature data from all images is used jointly in a hair growing process to construct smooth curves along the observed fibers. Finally, additional hairs are generated to fill in the unseen volume inside the hair. The method is demonstrated on both straight and wavy hair, with results suitable for realistic close-up renderings. These models provide the first views we know of into the 3D arrangement of hair fibers in real hair assemblies.

Previous research has shown that a global multiple scattering simulation is needed to achieve physically realistic renderings of hair, particularly light-colored hair with low absorption. However, previous methods have either sacrificed accuracy or have been too computationally expensive for practical use. In this paper we describe a physically based, volumetric rendering method that computes multiple scattering solutions, including directional effects, much faster than previous accurate methods. Our two-pass method first traces light paths through a volumetric representation of the hair, contributing power to a 3D grid of spherical harmonic coefficients that store the directional distribution of scattered radiance everywhere in the hair volume. Then, in a ray tracing pass, multiple scattering is computed by integrating the stored radiance against the scattering functions of visible fibers using an efficient matrix multiplication. Single scattering is computed using conventional direct illumination methods. In our comparisons the new method produces quality similar to that of the best previous methods, but computes multiple scattering more than 10 times faster.

Simulating multiple scattering correctly is important for accurate rendering of hair. However, a volume of hair is a difficult scene to simulate because scattering from an individual fiber is very structured and forward directed, and because the radiance distributions that arise from many such scattering events remain quite directional. For these reasons, previous methods cannot compute accurate images substantially faster than Monte Carlo path tracing.This paper proposes a new physically accurate method for rendering hair that is based on previous volumetric photon mapping methods. The first pass generates a photon map by tracing particles through the hair geometry, depositing them along paths rather than at scattering events. The second pass ray traces the hair, computing direct illumination and looking up indirect radiance in the photon map. Photons are stored and looked up in 5D position-direction space to allow for the very directional radiance distributions that occur in hair. Together with a new radiance caching method for fibers, our method simulates difficult scattering problems in hair efficiently and with low noise.The new algorithm is validated against path tracing and also compared with a photograph of light scattering in real hair.

Wood coated with transparent finish has a beautiful and distinctive appearance that is familiar to everyone. Woods with unusual grain patterns. such as tiger, burl, and birdseye figures, have a strikingly unusual directional reflectance that is prized for decorative applications. With new, high resolution measurements of spatially varying BRDFs. we show that this distinctive appearance is due to light scattering that does not conform to the usual notion of anisotropic surface reflection. The behavior can be explained by scattering from the matrix of wood fibers below the surface, resulting in a subsurface highlight that occurs on a cone with an out-of-plane axis. We propose a new shading model component to handle reflection from subsurface fibers, which is combined with the standard diffuse and specular components to make a complete shading model. Rendered results from fits of our model to the measurement data demonstrate that this new model captures the distinctive appearance of wood.