3.5. COORDINATE COLOR TRANSFORMATION

From expressions (3.4.7) it follows that the set of primary colors can be chosen in many ways. If color coordinates are known for one set of primary colors, then a simple coordinate transformation can be used to find color coordinates for another set [16]. Let be , , there is an initial set of primary colors with spectral densities , , . Intensities Equalizing Reference White denote by , and . Consider now another set of primary colors. , , having spectral densities , , . Reference white color which may differ from the original reference white equalized with intensities , , new colors. Arbitrary color has coordinates , , for the initial set of primary colors and , , for a new set. From the formula (3.4.10) you can get the matrix ratio

. (3.5.1)

Let us now establish the units of measurement for the new color coordinates. Taking instead of color new reference white color will get

, (3.5.2)

Where . Then substituting the new primary colors into the ratio (3.5.1) , , , will have

, (3.5.3a)

, (3.5.3b)

, (3.5.3b)

Where

, , .

The joint solution of the system of matrix equations (3.5.1), (3.5.2) and (3.5.3) gives the required relationship between the color coordinates for the original and the new sets of primary colors:

(3.5.4)

You can rewrite the relation (3.5.4) using the chromaticity coordinates , , New primary colors in the coordinate system of the original primary colors. In this case

, (3.5.5)

Where

,

,

,

,

,

,

,

,

,

,

,

,

.