In this paper we introduce B-spline illumination maps and their generalizations and extensions for use in realistic image generation algorithms. The B-spline lighting functions (i.e., illumination maps) are defined as weighted probability density functions. The lighting functions can be estimated from random data and may be used in bidirectional distributed ray tracing programs as well as radiosity oriented algorithms. The use of these lighting functions in a bidirectional ray tracing system that can handle dispersion as well as the focusing of light through lenses is presented.

Cook, Porter, and Carpenter coined the phrase "distributed ray tracing" to describe a technique for using each ray of a super-sampled ray tracing procedure as a sample in several dimensions to achieve effects such as penumbras and motion blur in addition to spatial anti-aliasing. The shade to be displayed at a pixel is a weighted integral of the image function. The purpose of using many rays per pixel is to estimate the value of this integral. In this work, a relationship between the number of sample rays and the quality of the estimate of this integral is derived. Furthermore, the number of rays required does not depend on the dimensionality of the space being sampled, but only on the variance of the multi-dimensional image function. The algorithm has been optimized through the use of statistical testing and stratified sampling.