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

[Keith Packard]

Around 17 o'clock on Oct 5, Ralph Corderoy wrote:

> >       r = 1 - c + ck - k
> >       r = (1 - c)(1 - k)
> 
> Sorry to take this off-topic, but why is the `+ ck' there?  Why isn't
> it
> 
>     r = 1 - c - k

I don't know -- I was only noticing that the two formula for CMYK->RGB
were the same.  It must come from a different CMY->CMYK conversion.
Working backwards from the CMY->RGB and CMYK->RGB conversions:

        ck = cyan component of cmyk
        k = black component of cmyk
        c = cyan component of cmy
        r = red component of rgb

        r = (1-ck)*(1-k)
        r = (1-c)
        (1-c) = (1-ck) * (1-k)
        1-c = 1 - ck - k + ck*k
        c = ck + k - ck*k
        c = ck *(1-k) + k

        ck = (c-k)/(1-k)

This formula clearly assumes a different mixing property of inks than your 
more obvious answer (ck = c - min(c,m,y)).  I don't find it hard to 
believe that some common printing technology is approximated more 
accurately with this formula.

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