Fast computation of tristimulus values by use of gaussian quadrature*

Abstract

In colorimetric work, the calculation of tristimulus values is typically accomplished by one of the standard numerical-integration schemes, such as Simpson’s rule. However, great computational savings can be achieved by use of a more-sophisticated approach. By computing the orthogonal polynomials associated with the CIE color-matching functions, the method of gaussian quadratures can be applied. For certain types of color-matching problems, the gaussian technique is at least twice as fast, for the same accuracy, as conventional methods.