How to reduce chroma of CIELAB color?

Given a CIELAB color (L* A* B* values), how can the chroma (saturation) be reduced?

Chroma can be calculated as follows:

Cab= sqrt(a²+b*²)

Let's say the output is 72. How do I transform variables a and b to force chroma to be eg. 43?

Short answer: to reverse polar coordinates back to cartesian space, you need to use the HUE correlate as well. Otherwise you won't know the direction the vector is in.

More Complete Answer:

To convert ab to hue:

    hueab = 180 * atan2( a , b ) / pi();

Then to convert hue and chroma back to L^*a^*b^*, then:

    a = Cab * cos((hueab * PI()) / 180);
    b = Cab * sin((hueab * PI()) / 180);

Saturation

You mention saturation. Chroma is not saturation.

• Saturation is the colorfulness relative to that color's own lightness.
• Chroma is the colorfulness relative to a separate reference white.

CIELAB does not do saturation, though other color models like CIELUV and CIECAM02 do.

CIELUV has the same L^* as LAB. But LUV is based on the 1976 UCS chromaticity diagram which uses uʹvʹ coordinates, and which is a simple projection of the 1931 chromaticity diagram. LUV multiples the uʹvʹ each by 13L^*, to make them u^*v^*.

You create hue and chroma the same way as LAB, but with LUV you can create a useful saturation correlate, which is not really possible in LAB.

To create saturation from chroma_u^*v^*:

    Suv = Cuv / Lstar;

Trivial, and to get saturation back to chroma, obviously:

    Cuv = Suv * Lstar;

Other Models

CIELAB and CIELUV both came out in 1976 (about the same time as the first Star Wars). Today we have much more accurate models like CIECAM02, CAM16, J_za_zb_z, ZCAM, etc. I encourage your to take a look at some of them.

Also, you might be interested in this CIELUV implementation, HSLUV which has some benefits including indication of the gamut limits while choosing colors.

https://www.hsluv.org