What are chromaticity coordinates?

There is often a need for an intuitive interpretation of colour specification in terms of tristimulus values. This is one reason why the three-dimensional colour colour space defined by X, Y, and Z is often transformed and plotted in terms of a chromaticity diagram. Chromaticity coordinates x, y, and z are derived by calculating the fractional components of the tristimulus values thus:

x = X/(X + Y + Z),
y = Y/(X + Y + Z),
z = Z/(X + Y + Z).

Since by definition x + y + z = 1, if two of the chromaticity coordinates are known then the third is redundant. Thus, all possible sets of tristimulus values can be represented in a two-dimensional plot of two of these chromaticity coordinates and by convention x and y are always used. A plot of this type is referred to as a chromaticity diagram. The use of chromaticity diagrams has not enabled three-dimensional data to be compressed into two-dimensional data. Consider two samples A and B having specification:

Sample A: X = 10, Y = 20, Z = 30
Sample B: X = 20, Y = 40, Z = 60

Samples A and B have identical chromaticity coordinates but different tristimulus values. The difference between the two samples is one of luminance and B would probably appear brighter than A if the two samples were viewed together. A complete specification using chromaticity coordinates therefore requires two chromaticity coordinates and one of the tristimulus values.