complementary colors in Julia (RGB versus Lab colorspace)

Question

Complementary (light) colors are defined as : "light colors such that, when added, mix to white (or neutral)".

Thus, in RGB:, let c(R,G,B) be a light color; then  cC(Rc,Gc,Bc) are complements iff R+Rc=G+Gc=B+Bc this means that there is a segment of complementary colors defined by two points: (1-R,1-G,1-B) and (m-R,m-G,m-B) where m=maximum(R,G,B).

If two colors are complementary, they should remain complementary in any color space. Shouldn't they? Thus if the Julia conversion of c(R,G,B) in Lab is c(L,a,b), converting cC(Rc,Rc,Gc) in Lab (in Julia) should give c(L,-a,-b). In general, it does not.

I have tried to convert several complementary pairs from RGB to Lab using the Julia function convert(Lab,c) but the result does not produce pairs of symmetrical values. How come? Is is a question of white point? If yes, which one to use and how to introduce it in the conversion function?

Answer 1

As usual, colors are tricky. After playing around with complementary color definitions, I think your best bet is to define complementary colors in HSV space. In code this can be as follows:

using Colors

function complement_hsv(c)
    hsvc = HSV(c);
    if hsvc.h >= 180
        return typeof(c)(hsvc.h - 180, hsvc.s, hsvc.v)
    else
        return typeof(c)(hsvc.h + 180, hsvc.s, hsvc.v)
    end
end

This gives the added bonus (not true in OP method) of:

complement_hsv(complement_hsv(c)) == c

And in Lab space, the L stays roughly the same, and the a-b roughly reverse sign.

UPDATE:

If the desired complementary colors are needed to have the simple Lab property mentioned, this can be defined explicitly:

function complement_lab(c)
    labc = Lab(c);
    return typeof(c)(labc.L, -labc.a, -labc.b)
end