4 - Mathematical terms

Abstract

This chapter defines the basic terms, concepts, and notations used in describing light and materials. One needs physically based models with parameters with physical meaning so that measuring materials, adjusting, and reusing them in scenes produce effects consistent with what one observes in the real world. To make physically based numerical definitions, there is a need to define various expressions for how incident light energy is distributed by a material with respect to position, direction, and wavelength. For many years, computer graphics systems used ad hoc descriptions of shades and lights making it difficult to compare and combine methods across different vocabularies, units, and scales. Adopting the standard terms used by the illumination and radiative transfer communities advanced successful realistic modeling. The key quantity in defining light transfer in a particular direction is radiance. The key quantity for expressing the directional effect of materials on the incident radiance is the bidirectional reflectance distribution function (BRDF). There are many materials that require an extended definition of scattering beyond the BRDF, but they are easily understood once radiance and BRDF are defined. While understanding the definitions of radiance and reflectance can be challenging, it is the key to being able to understand material models.