As Im still reading through handprint, I'm to the part where the "cone excitation space" is converted in the "chromaticity plane" by taking away luminance or dividing each of the three cone types by the sum of all three. I am trying to understand exactly what is happening here but I'm really confused. Are we turning a 3d graph into a 2d graph? How does this diagram show brightness?
Chromaticity shows the proportion that each component (L,M,S or X,Y,Z etc., depending on color space) contributes to the whole stimulus. You can think of it like a percentage.
Here's an example using XYZ. Let's say you're looking at someone's face, and the X,Y,Z of the skin in a certain light is 182, 38, 28. The total is 182+38+28 = 248. The chromaticity of the skin would be:
x = 182/248 = 0.7339 (or 73.4%)
y = 38/248 = 0.1532 (or 15.3%)
z = 28/248 = 0.1129 (or 11.3%)
Then a cloud passes across the sun and the light is cut in half. The X,Y,Z are also cut in half, to 91, 19, 14 respectively. The total now is 124, and the chromaticity is:
x = 91/124 = 0.7339
y = 19/124 = 0.1532
z = 14/124 = 0.1129
So the chromaticity doesn't change. It is independent of exposure. Chromaticity represents that part of the color that doesn't change with lightness/brightness: the combination of hue and saturation.
If you plot chromaticities x,y,z in the 3-dimensional X,Y,Z space, they all lie on a triangular plane. The standard CIE chromaticity diagram only plots the two dimensions x and y, as z is implied (since x + y + z = 1). Brightness or lightness is not shown on the chromaticity diagram.
I will add that, unlike a lot of the concepts in this thread, chromaticity is actually pretty relevant for photographers. When you change exposure in the camera, chromaticity does not change in the raw file. But when you adjust exposure in your image editor, chromaticity is not necessarily preserved. Some editing tools change the hue or saturation while you change lightness. Luminosity Blend Mode doesn't preserve chromaticity. Some color spaces don't preserve chromaticy, either, such as in CIELAB when editing the lightness channel. When chromaticity isn't preserved, you get those often unwanted changes in saturation and hue that make images look less realistic.