Approximate methods for light transport in volumetric materials

An object's appearance is affected both by light reflecting from its surface and light propagating through its volume. Simulating such light-object interaction is necessary when creating realistic computer graphics images. While for some objects surface reflection dominates, for many objects multiple scattering within the volume contributes significantly to visual appearance. Since the effects of multiple scattering are very costly to compute and simulate, we describe several approximations for light transport in volumetric materials that are especially applicable for depiction of natural materials such as water and clouds. These approximations differ by assuming different levels of complexity in the medium being approximated. First, the object is assumed to be a uniform body of water illuminated from above. Here the specificity of geometry and material composition can be leveraged to yield a very efficient approximation. Second, the object is allowed to be composed of layers of varying optical properties, and the object's geometry is of low curvature relative to the layer thickness. Finally, the general case of geometry and optical properties are assumed and the mathematical tool of path integrals is used to develop approximations that characterize the path that contributes the most to the final intensity and give a solution in terms of the most probable path and quadratic fluctuations around this path. A hierarchical version of this approximation is also developed. All of these methods approximate the appearance of light transport within the volume of materials equation with different assumptions ranging from a very specific medium to very general materials that can be applied to a variety of rendering problems. These methods provide insights into light propagation that could lead to further approximations that are tailored to the amount of generality of particular problems.