Trichromatic approximation for computer graphics illumination models

Abstract

The complexity of computer graphics illumination models and the associated need to find ways of reducing evaluation time has led to the use of two methods for simplifying the spectral data needed for an exact solution. The first method, where spectral data is sampled at a number of discrete points, has been extensively investigated and bounds for the error are known. Unfortunately, the second method, where spectral data is replaced with tristimulus values (such as RGB values), is very little understood even though it is widely used. In this paper we examine the error incurred by the use of this method by investigating the problem of approximating the tristimulus coordinates of light reflected from a surface from those of the source and the surface. A variation on a well known and widely used approximation is presented. This variation used the XYZ primaries which have unique properties that yield straightforward analytic bounds for the approximation error. This analysis is important because it gives a sound mathematical footing to the widely used method of trichromatic approximation. The error bounds will give some insights into the factors that affect accuracy and will indicate why this method often works quite well in practice.