I understand that the primary colors are unable to match the test color on the left because the color is out of gamut. Is there a basis of colors that can match any color that humans can perceive? What makes the primary colors the "primary" colors?
It always seemed a little weird to me that three seemingly random colors could be combined to form any other color. I've heard this fact repeated ad infinitum since elementary school art class, and this is the first time I've seen a claim to the contrary, of the existence of a color that can't be created by combining the three primary colors. I wonder if four primary colors is enough to span the entire visible spectrum of light?
A fourth color won't necessarily help this problem in general - for example, if your fourth color is a positive linear combination of the previous three, then it won't be able to help you reach any colors that were out of gamut for the original three.
Here's an interesting graph for illustrating possible color spaces: https://upload.wikimedia.org/wikipedia/commons/thumb/d/d3/CIExy1931_srgb_gamut.png/240px-CIExy1931_srgb_gamut.png
The triangle represents the RGB color space an everything outside of it (the grayed area) is out of gamut
The way I understand this is that the primaries still span the 3D space but because we can't output a negative amount of energy it is out of gamut. Shifting p2 to the other side is the same as having a negative amt on the input side.
I am still having a hard time understanding why the negative light gets applied to the left side. Doesn't this change the color we are trying to find and what does it even mean to have a negative value on the right.