# How Negative Color Value is accepted in Tristimulus Values for Mixing Colors?

I read a chapter about Trichromatic Theory of Color Mixture (Yao Wang, et all. 2001), about how we can produce most colors by mixing 3 primary colors. And the amount of three primary colors required to match the target color is called Tristimulus values. And we can produce a color by mixing primaries following this equation :

$$C = { \sum_{k=1,2,3} T_k C_k },$$ where :

• C = Given color
• Ck, k = 1,2,3, represents the color of primary sources
• Tk = Amount of primary colors required to match the color (tristimulus value)

I believe in Trichromatic color theory related to human vision system, primary colors depend on the source, either lights (perceived wavelength, ranged from 380nm-780nm) or digital color (RGB ranged from 0-255), their value can't be negative.

The book mentioned :

"In general, some of Tristimulus value can be negative."

My question is, if primary color can't be negative, how is it that tristimulus value which is the amount of primary color to make another color can be negative ?

## 1 Answer

There is a good explanation in wiki of CIE 1931 color space:

" Most wavelengths stimulate two or all three kinds of cone cell because the spectral sensitivity curves of the three kinds overlap. Certain tristimulus values are thus physically impossible, for example LMS tristimulus values that are non-zero for the M component and zero for both the L and S components. Furthermore, LMS tristimulus values for pure spectral colors would, in any normal trichromatic additive color space, e. g. the RGB color spaces, imply negative values for at least one of the three primaries because the chromaticity would be outside the color triangle defined by the primary colors. To avoid these negative RGB values, and to have one component that describes the perceived brightness, "imaginary" primary colors and corresponding color-matching functions were formulated. The CIE 1931 color space defines the resulting tristimulus values, in which they are denoted by "X", "Y", and "Z". In XYZ space, all combinations of non-negative coordinates are meaningful, but many, such as the primary locations [1, 0, 0], [0, 1, 0], and [0, 0, 1], correspond to imaginary colors outside the space of possible LMS coordinates; imaginary colors do not correspond to any spectral distribution of wavelengths and therefore have no physical reality. "