Color Gamut and Gamut Mapping
For any printing device, there will be physical limits to the range of color that can be reproduced. In the illustrations below, there is no way to mix the "dull" inks to produce the pure cyan or yellow, or even the black, of the "bright" inks. This principle applies as well to the red, green, and blue of photographic film and television screens, and in fact applies to all color reproduction systems.
On the other hand, it is almost always possible to mix the bright inks to produce any color that can be produced by the dull inks. That is essentially what is happening with colorants on your computer monitor right now, as you view the above illustration. The full range of colors that can be produced by any color reproduction system is called the color gamut of that system.
Curiously, this very real phenomenon is made a scapegoat for all kinds of other deficiencies in color management. For instance, we've actually heard it blamed for an inability to match SWOP printing values with the "extreme" gamut inks sold by some large–format inkjet manufacturers. Nothing could be further from reality. With real color management of the sort discussed elsewhere on this web site, one always wants the most "extreme" gamut available. Simulation of other systems, such as SWOP, is thereafter simple because all of the desired colors are available.
It is popular to draw a picture of available colors (a color "space") as a colored disk, and to then draw out the available gamut as a polygon on that illustration. In the illustration below, we've actually shown two polygons. Each of them has six points, corresponding to six "primary" colors: cyan, magenta, yellow, red, green, and blue. The area inside a polygon represents all the colors that can be achieved with that particular set of inks. It's a picture of the gamut.
In this illustration, the black polygon corresponds to the bright inks, and the white polygon corresponds to the dull inks. The colored disk on which the polygons are displayed is typically "plane" from within a CIE L*a*b color space. This is a handy way that color scientists display the relationship between the gamuts of two different color reproduction systems. The fact that all the colors achievable by the dull inks are also achievable by the bright inks is nicely illustrated. The fact that the bright inks can achieve colors that can't be achieved by the dull inks is likewise illustrated.
When we are limited to printing with dull inks, and we're asked to reproduce an image that is specified for the bright inks, we're forced to make some sort of compromise. This is called gamut mapping.
One simple solution is to move all the points outside the white polygon directly inward to the nearest point on that polygon, while matching all other points as accurately as possible. This provides the best possible match to all colors that can be accurately matched, and is great for hitting spot colors, but it tends to produce lousy reproductions of photographs.
Consider a photograph of an apple in which the reds of the highlights all have to be moved, and that by these rules, they're all moved to the same point on the white polygon. As we view the photograph, we'll see a terrible "fringe" surrounding the highlight as the area of out–of–gamut colors that have been run together transitions to the area where more accurate color reproduction is possible.
Perceptual (or Photometric) Correction
A more satisfactory solution would be to somehow "deform" the entire surface of the above diagram so that all points are moved into the white polygon, while avoiding "clipping" colors so that colors that differed in the original are knocked down to be the same color in the reproduction. Colors that are within the reach of the dull inks (inside the white polygon) will be less accurately reproduced, but your reproductions will be free of the nasty "fringes" described above.
There are an infinite variety of ways to perform these "deformations" of the color space, and this is the real art of color management. The beauty of standards for exchanging these things, such as the ICC profile standard, is that if you don't like one supplier's art, it is easy to substitute another's, or to substitute your own.
When Gamut Mapping is Not the Issue
Suppose that you actually have the bright inks and you've been asked to reproduce a picture specified for the duller inks. This is the case when your printer is equipped with "extreme" inks and you're being asked to reproduce color specified with good old SWOP printing standards. The entire white polygon is now contained within the polygon of the inks that you've got for printing, and you can hit all the colors. The colorimetric and perceptual corrections are the same, art is not called for, and science reigns!
If you find that you can't do this, don't go back to dull inks—get better color management. Solving the problem by going back to dull inks is like buying an abacus to replace your computer. There is real color management available, and it's reasonable for you to insist on using it.