# Scaling of the CIE RGB color matching functions

In the CIE color system, the RGB color matching functions look like this when plotted (I'm unsure what the unit of the Y axis is) https://en.wikipedia.org/wiki/CIE_1931_color_space#CIE_RGB_color_space

I am trying to understand how these color matching functions relate to the graph of chromaticity coordinates.

Here are the chromaticity coordiantes as seen in the book Measurement of Color

• This may be off topic, since generally the scope of our site doesn't extend to visual perception. But I'm not sure; this is closer to being physics than the average perception question. We'll see what others say. – David Z Feb 28 '16 at 12:54

The color matching functions (in the first chart) tell you in absolute quantities how much light from each primary is needed to match a reference light. The scalar quantities are known as tristimulus values.

The chromaticity coordinates are the color matching functions normalized so that the sum of each value adds up to 1.

This gives you a better way to visualize the relative quantities of lights involved in a color match.

RGB = tristimulus values (first chart)
rgb = chromaticity coordinates (second chart)

r = R/(R+G+B)
g = G/(R+G+B)
b = B/(R+G+B)


for example the chromaticity coordinates show you that to match 380nm light you need much more blue primary light than red primary light.

The color matching functions show you that despite needing more blue than red, in absolute terms you need very little of either because the eye is not very sensitive to 380nm light.

In order to visualize the color matching functions you need a 3D graph (each primary is a dimension). The normalized chromaticity coordinates allow you to create a 2D visualization (the 3rd dimension can be derived from the other 2 since they all sum to 1).

The 2D plot is called a Chromaticity diagram, here's the diagram for the above rgb chromaticity coordiantes. https://en.wikipedia.org/wiki/CIE_1931_color_space