The C.I.E Primaries

The Commission Internationale d'Eclairage derived a new set of primaries using the blue, green, and red primaries in both positive and negative combinations. This new set of primaries, called X, Y, and Z, have the following properties:

1. They always produce positive tristimulus values.
2. It is possible to represent any color in terms of these primaries.
3. They were derived so that equal values of X, Y, and Z produce white.
4. They were arranged so that a single parameter Y determines the luminance of the color.
5. They are related to the sensitivity of the human eye by the use of color matching functions which match to the C.I.E. 1931 Standard Observer.

The C.I.E. Color Matching Functions

If the spectral power distribution (SPD) for a colored object is weighted by these curves, the CIE chromaticity coordinates can be calculated.

Additive Color Mixing with CIE

The result of adding two colors of light can be worked out as a weighted average of the CIE chromaticity coordinates for the two colors. The weighting factors involve the brightness parameters Y. If the coordinates of the two colors are

then the additive mixture color coordinates are

This linear procedure is valid only if the colors are relatively close to each other in value.