[Groff] Re: CMYK <-> RGB

[Keith Packard]

Around 17 o'clock on Oct 4, Werner LEMBERG wrote:

>   CMYK_ADOBE_COLORSPACE:
> 
>     r = (k*c)/maxval;
>     g = (k*m)/maxval;
>     b = (k*y)/maxval;

This one is clearly wrong -- CMYK is traditionally a subtractive space.


  CMYK_NORMAL_COLORSPACE:

    r = ((maxval-k)*(maxval-c))/maxval;
    g = ((maxval-k)*(maxval-m))/maxval;
    b = ((maxval-k)*(maxval-y))/maxval;

    r = maxval - min(maxval, c*(maxval-k)/maxval + k);
    g = maxval - min(maxval, m*(maxval-k)/maxval + k);
    b = maxval - min(maxval, y*(maxval-k)/maxval + k);

These are the same.  Proof:

(take maxval == 1, 0 <= c,m,y,k <= 1)

        r = 1 - min (1, c * (1-k) + k)

Given 0 <= k <= 1, then for any Q <= 1:

        Q * (1 - k) + k <= (1 - k) + k =1

thus
        c * (1-k) + k <= 1

Hence:

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

I see no conflict here, just bogus code in groff.

-keith