Mixing two RGB color vectors to get resultant

Question

I am trying to mix two source RGB vectors to create a third "resultant vector" that is an intuitive mix of the first two.

Ideally, I would be able to emulate "real paint mixing characteristics", but for simplicity, I am trying to find a method where the resultant looks intuitively like what you'd get from combining the two source rgb's.

minimally, these characteristics:
RED + BLACK = DARK RED
RED + WHITE = LIGHT RED

optimally, also with real paint characteristics:
RED + BLUE = PURPLE
RED + YELLOW = ORANGE
(etc)

--

I am currently doing this the "lazy way" by adding the two source RGB vectors/255, then normalizing (and multiplying by 255). So, using this: [Red = <1,0,0> * 255] + [Blue = <0,0,1> * 255] gives Magenta=<1,0,1>/sqrt(2) * 255, though the other colors are less intuitive or even visible... I need a better method! Please help :-)

Solution 1

Is what you suggested the same as a weighted average?

Average R = w1*R1 + w2*R2 + w3*R3 + ... + wn*Rn

Average G = w1*G1 + w2*G2 + w3*G3 + ... + wn*Gn

Average B = w1*B1 + w2*B2 + w3*B3 + ... + wn*Bn

The w's are the weighting fractions and the sum of them is 1.

R1 is the red component of the first color to mix, for example.

So if you wanted to mix two colors evenly, it would be:

Average R = 0.5*R1 + 0.5*R2

Average G = 0.5*G1 + 0.5*G2

Average B = 0.5*B1 + 0.5*B2

As for mapping the resultant color to a named color ("dark red") maybe just do a lookup table and pick the closest one?

Solution 2

The problem is that you're trying to relate two different color theories. RGB is additive color theory (colored light is emitted from the source). In this case the more of the spectrum you add to the mix, the closer you get to white.

For "paint mixing" you need to emulate subtractive color theory which governs the way reflected colors are mixed. (i.e. reflected light such as paints, different surfaces etc.) Here's an overview.

The JavaScript on this page is a clue as to how you might proceed in converting RGB to CMYK.

Solution 3

Mixing RGB colors to simulate subtractive color mixture (i.e., paint-like mixture) can be done by transforming the RGB values to spectral reflectance curves, then doing the mixture there. This question is very similar to another, stackoverflow.com/questions/10254022/, where the solution is discussed in more detail.

Solution 4

I think you should really define what is "+" in your color scheme.

Based on your requirements, I've translated them into estimated hex color codes, (rgb represention can be deduced easily).

RED     + BLACK   = DARK RED  
#ff0000 + #000000 = #800000
RED     + WHITE   = LIGHT RED
#ff0000 + #ffffff = #ff8080

optimally, also with real paint characteristics:
RED     + BLUE    = PURPLE
#ff0000 + #0000ff = #800080
RED     + YELLOW  = ORANGE
#ff0000 + #ffff00 = #ff8000

I do not see a definite pattern which you can work out some formulas to achieve that.

John's and Nils' methods probably will come close to the colors but probably not to the exact values. I suggest you give theirs a try.

EDIT:
Updated the wrong color codes. Well it does made a lot more sense now.

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Comments

[yos]

How do you determine the w's or the W matrix to be able to mix rgb (or cmyk) like paint?

[Mark Ransom]

If you're mixing 2 colors, the W is 1/2 or 0.5, exactly as the answer suggests.

[Mark Ransom]

Yes, if you fixed yellow=#ffff00 and orange=#ff8000 and light red=#ff8080, the pattern would become clear.

[Mark Ransom]

The question asks about paint mixing, but the examples all seem more related to RGB mixing. I find CMYK mixing to be very counter-intuitive.

[Paul Sasik]

i interpreted the question to be asking about mixing RGB (additive) but getting CMYK (subtractive) results.

[Carl Smith]

Just to be clear, if the weights are equal, you could just leave them, and divide the result by the number of colors mixed instead ((R1 + R2 + R3) / 3). When they are unequal, their sum should equal 1. The point is to get a mean average.