Re: [Groff] Re: CMYK <-> RGB

[Larry Jones]

Ralph Corderoy writes:
> 
> Sorry to take this off-topic, but why is the `+ ck' there?  Why isn't
> it
> 
>     r = 1 - c - k
> 
> on the basis of cmy to cmyk is
> 
>     k = min(c, m, y)
>     c, m, y = c - k, m - k, y - k

Because it isn't really that simple in real life -- the more black ink
you have on the page, the more colored ink you need to add to get it to
look colored rather than just black.  So, a more accurate conversion
from CMY to CMYK is:

        k' = min(c, m, y)
        c' = (c - k')/(1 - k')
        m' = (m - k')/(1 - k')
        y' = (y - k')/(1 - k')

(with some convention for the 0/0 case; both 0 and 1 are common).

For very bright colors (small k), the result is very close to the simple
formula, but for very dark colors (large k), the amount of colored ink
is much larger.  Inverting this conversion is what gives rise to the
confusing +ck term -- dark colors aren't really as dark as the simple
formula implies.

-Larry Jones

I keep forgetting that rules are only for little nice people. -- Calvin