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XYZ and xyY

Tristimulous Values ⇄ Chromaticity

XYZ to xyY​

If X = Y = Z = 0, x and y are set to the chromaticity coordinates of the reference white.

x={WX if X=Y=Z=0XX+Y+Z otherwise y={WY if X=Y=Z=0YX+Y+Z otherwise Y=Y\begin{align*} x &= \begin{cases} W_X & \text{ if } X = Y = Z = 0 \\ \frac{X}{X + Y + Z} & \text{ otherwise } \end{cases} \\ y &= \begin{cases} W_Y & \text{ if } X = Y = Z = 0 \\ \frac{Y}{X + Y + Z} & \text{ otherwise } \end{cases} \\ Y &= Y \end{align*}

xyZ to XYZ​

X={0 if y=0x⋅Yy otherwise Y=YZ={0 if y=0(1−x−y)⋅Yy otherwise \begin{align*} X &= \begin{cases} 0 & \text{ if } y=0 \\ \frac{x \cdot Y}{y} & \text{ otherwise } \end{cases}\\ Y &= Y \\ Z &= \begin{cases} 0 & \text{ if } y=0 \\ \frac{(1 - x - y) \cdot Y}{y} & \text{ otherwise } \end{cases} \end{align*}