RGB Colour Model
Red Green Blue

CMYK Colour Model
CIELAB Colour Model
CIEXYZ Colour Model

Munsell Colour Model
HSL Colour Model
HSB Colour Model

CMY(K) Colour Models

Yellow (Jaune)
blacK (Noir)

CMY to CMYK - The Idea of the K or Black is to replace the even amounts of all the colours with black leaving the difference for a more defined image.

K = Minimum of C,M,K
C = (C-K)/(1-K)
M = (M-K)/(1-K)
Y = (Y-K)/(1-K)

Here we need to simulate the black back into the separate colours.
This may be needed where the ink limits need adjusting for printing.
C = C*(1-K)+K
M = M*(1-K)+K
Y = Y*(1-K)+k

converting between RGB and CMY(K) is easy but note that these direct conversions should be done between colour profiling.

C = (1-R)
M = (1-G)
Y = (1-B)

R = (1-C)
G = (1-M)
B = (1-Y)

Like with the CMY calculations we looked for the smallest amount of colour for setting black in RGB we are looking for the most and then converting for our calculation.

K = (1-Maximum R,G,B)
C = ((1-R)-K)/(1-K)
M = ((1-G)-K)/(1-K)
Y = ((1-B)-K)/(1-K)

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