Analytic light transport approximations for volumetric materials

Subsurface scattering and light transport in volumetric media are critical to achieve a realistic depiction of a material. We describe several analytical approximations and methods for volumetric light transport in media of various optical properties that are efficient and easy to compute. Most natural materials exhibit a sudden surge in brightness called the opposition effect around the zero phase angle, where incident and viewing directions coincide. We present an approximation to the opposition effect in a particulate medium using a few physically realistic mathematical approximations. These analytical approximations can be used as tools or as a starting point for modeling the appearance of complex volumetric materials such as biological materials(skin, leaves) or inorganic materials (snow, clouds, rocks, paint). We demonstrate these approximations for several natural materials that exhibit substantial volumetric light transport and show how to use them to model complex materials.