Simple Analytic Approximations
to the CIE XYZ Color Matching Functions
Authors: Chris Wyman
Peter-Pike Sloan
Peter Shirley

Editor: Larry Gritz
Sony Pictures Imageworks
Editor-in-Chief: Morgan McGuire
Williams College & NVIDIA


We provide three analytical fits to the CIE , , and color matching curves commonly used in predictive and spectral renderers as an intermediate between light spectra and RGB colors. Any of these fits can replace the standard tabulated CIE curves. Using tabulated curves can introduce typos, encourage crude simplifying approximations, or add opportunities to download curves from sources featuring inconsistent or incorrect data. Our analytic fits are simple to implement and verify. While fitting introduces error, our fits introduce less than the variance between the human-subject data aggregated into the CIE standard. Additionally, common rendering approximations, such as coarse spectral binning, introduce significantly more error. We provide simple, analytic fits in Equations 2 and 3, but even our more accurate fit in Equation 4 only requires ten lines of code.

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Citation: Chris Wyman, Peter-Pike Sloan, and Peter Shirley, Simple Analytic Approximations to the CIE XYZ Color Matching Functions, Journal of Computer Graphics Techniques (JCGT), vol. 2, no. 2, 1-11, 2013. Available online

Copyright: © 2013 Wyman, Sloan, and Shirley

Received: 2012-11-01; Recommended: 2013-01-14; Published: 2013-07-12