# CIELuv Color Model

## Chromaticity coordinates

Chromaticity coordinates $u'$ and $v'$ are the CIE 1976 Uniform Chromaticity Scales coordinates of the color. $u'_n$ and $v'_n$ are the coordinates of the reference white. The conversion from tristimulus values to $u'$ and $v'$ is $$u' = \frac{4X}{X+15Y+3Z} \; \; \; \; v' = \frac{9Y}{X+15Y+3Z}$$ $L^*$, $u^*$, and $v^*$ represent the color's lightness, red/green, and yellow/blue.

## Tristimulus values

Tristimulus values $X$, $Y$, and $Z$ are the relative luminances of total luminance $Y$, blue stimulation $Z$, and $X$ is a linear combination of the cone response curves, all from 0 to 100.

The conversion from tristimulus values to L*, u*, and v* is $$L^* = \left\{\begin{matrix} 116 \left ( \frac{Y}{Y_n} \right )^{1/3} -16 ;& \frac{Y}{Y_n} > 0.008856\\ 903.292 \left ( \frac{Y}{Y_n} \right ); & \frac{Y}{Y_n} \leq 0.008856 \end{matrix}\right.$$ $$u^* = 13L^*\left ( u' - u'_n \right ) \; \; \; \; v^* = 13L^*\left ( v' - v'_n \right )$$ After performing either conversion, the specified color is plotted on the CIELuv diagram.

References:
1. Color Vision and Colorimetry: Theory and Applications, Second Edition by Daniel Malacara, SPIE Press, 2011

## 1976 CIELuv Diagram 