# RGB basis?

1. Jul 14, 2009

### Enjoicube

Since prime colors cannot be created by any combination of any other colors, and since composite colors are combinations of the prime colors by definition, does this mean that the prime colors could form a basis for a space of colors? If you split up a color into components, like real vectors, then you can express composite colors as combinations of the prime colors. Does this idea make any sense? Because I found that it correctly predicted the resulting colors when I combined colors in a spectroscopy lab.

2. Jul 14, 2009

### mgb_phys

Yes, take a look at Gamut, 'color space' and 'color triangle' eg on wiki.

3. Jul 14, 2009

### Enjoicube

Very very odd and interesting. Seems that Yellow, Magenta and plain blue can also be a basis, as

Cyan=Red+Green
Magenta=Green+Blue
Blue=Blue

Now, if these are expressed in matrix form, as

(1,1,0)
(0,1,1)
(0,0,1)

Then they are in echelon form (and expressed in terms of basis vectors), and so they are linearly independent. This makes me asky why some printers use Cyan Yellow and Magenta instead of Red Green Blue?

4. Jul 14, 2009

### mgb_phys

You can pick any three colors and define a color space - there is nothing particulalry special about RGB except that it roughly matches your eye's response.
The reason for printers using CMY is that printing involves reflected light, if you view a picture in white light then eg. cyan and megenta together will absorb all wavelengths except blue - giving you a blue area.

5. Jul 14, 2009

### HallsofIvy

It would help if you would explain what you mean by "prime color" and "composite color". Basically, because the human eye has three different kinds of "cones" that primarily distinguish three different kinds of color, colors seen by the human eye can be thought of as a three dimensional vector space. Of course, there are an infinite number of different bases for a three dimemsional space. That has nothing to do with the usual concepts of "prime" or "composite" numbers.

6. Jul 14, 2009

### DaveC426913

There are many sets of primary colours. Two of the most common ones are:
red, green, blue - the additive primaries of light
With all three set to zero, you get black; all three at max you get white.

cyan, magenta, yellow - the subtractive primaries of pigments
With all three set to zero, you get white*; all three at max you get black**.

*the colour of the background
** pigments are not perfect, so a true black can't be printed. This is why print primaries add a black: i.e.: CMYK. In fact, the entire colour space of printing is much smaller than the colour space of RGB. There's a whole science and industry to cramming the ideal RGB into the realistic of CMYK.

And, as others have pointed out, it is no coincidence that RGB are the three colours associated with human eyesight.

Wait, you know all this... I've come late to the table...

7. Jul 15, 2009

### Enjoicube

Yes, now I realise that RGB is not the only basis for color space, and of course three dimensional vector space has infinite number of different bases, however, for example, it would be quite thoughtless to choose {34(x^2)+23x+5,87x+54,798} as a basis for the space of polynomials of degree 2, although it is a linearly independent set and spans the space. It makes sense that we would choose a basis that our eyes are sensitive to such as RGB or CYM. Primary colors is a very misleading definition though, as when taught in primary school, it is said in such a way that implies RGB are the only primary colors, I guess that is where my thinking got off track. Thank you all for your responses, I have learned quite a bit here.

Edit: I just researched the cones of the eye, apparently their sensitivity peaks at roughly RGB, this makes sense now.

Last edited: Jul 15, 2009