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
The first plot is the (normalized) raw color-matching data from which the CIE 1931 XYZ space is derived. They have been normalized to have equal areas under the curves. If you multiply the green by 1.3751 and the red by 72.0962, you will recover the actual intensities of the red, green, and blue primary monochromatic sources (at wavelengths 700., 546.1 and 435.8 nm) required to match a unit intensity monochromatic source at wavelength λ. Notice that at those primary wavelengths, two of the curves are at zero, as you would expect. The red primary had to be at a high intensity since the sensitivity of the eye is so low at that wavelength (700 nm).
The second plot is the tricromatic coefficients. If the first plot is of Wi(λ), where i is R, G, or B, then the second plot is a plot of Wi(λ)/ΣiWi(λ). As you would expect, at the primary wavelengths, one curve is at unity, the other two at zero, and the sum of all the curves is unity at every wavelength.
For the third plot, the raw data was re-measured using different primaries at 650, 530 and 460 nm. The trichromatic coefficients were re-calculated from this data, and are shown in the third plot. This is from the paper "A re-determination of the trichromatic coefficients of the spectral colours" by Wright (1929).
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
