Mixing it up with the COLORCUBE by Ken Davies

The 3D constuction of the COLORCUBE places individual colors in a matrix according to their CMY input content. Color mapping and navigation through this color space is demonstrated in the following document on paint mixing where each of the colors shown above are created from the primary colors. Learn more about Color Mixing from the Teachers' Guide.

Contents

• Introduction
• 3D Ordering
• Color Identification
• Calculating Base Content
• Simple Color Runs
• Maximizing Color Space

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Color Theory
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Introduction

The COLORCUBE defines the set of colors that can be reproduced by mixing varying proportions of three primary colors. In the subtractive color space, these primaries are cyan, magenta and yellow, plus white as the base color.

The color space is called subtractive because white, its base color, reflects all spectral wavelengths and any color added to white absorbs or "subtracts" different wavelengths. The longer wavelengths of the visible spectrum, which are normally perceived as red, are absorbed by cyan. Magenta absorbs the middle wavelengths (green) and yellow absorbs the shorter wavelengths of the visible spectrum (blue-violet). Mixing cyan, magenta and yellow together "subtracts" all wavelengths of visible light and as a result, we see black.

Every color medium that uses paint or color pigment is said to operate in the subtractive color space. Understanding how color behaves in this system is essential for anyone who prints, paints or reproduces color documents. Learning the "hows and whys" about color is made simple by the COLORCUBE model. Unlike most other color models, this 3D representation of color defines color based on the input values of primaries, not by the measured output value. This document illustrates, using paint examples, how this model allows colors to be naturally described as products of cyan, magenta and yellow (CMY) rather than as colors from a restricted list or subjective interpretations.

3D Color Space

The underlying structure of the COLORCUBE can be described as a series of intersecting color planes. The planes are arranged along an axis and progress from "no primary content" (0%) to "maximum primary content" (100%) for each of the three CMY primary colors. Each reproducible color is geometrically placed in a 3D matrix based on the proportional quantities of primary CMY inputs used to mix each color.

For example, the white cube in the diagram to the right contains zero cyan. Progressing to the right, each plane contains incremental increases of cyan. To simplify this concept, we will equate planes of color to drops of paint. Therefore, each series of planes will run from 0-4 inclusive and correspond to a like number of paint drops.

Using paint pigments for illustrating color concepts will require us to operate in the subtractive color space. Please keep in mind other color media will involve slight variations in the following color mixing procedures.

As CMY pigments are added to a white base medium, the resulting color can be predicted using the COLORCUBE. Beginning at the white cube, simply count the number of planes crossed along the corresponding CMY axis.

Color Identification

Each color within the COLORCUBE is uniquely defined by the intersection of three planes. This feature of the model provides coordinates for each color and a basis for both color naming and color mixing.

The position of a color within the COLORCUBE identifies its mixing formula. For instance, a color that is located in yellow plane 3, cyan plane 3, and magenta plane 1 can be defined as containing 3 drops of yellow paint, 3 drops of cyan, and 1 drop of magenta. This is distinct from the color located at yellow plane 3, cyan plane 3 and magenta plane 0 as the latter has no magenta content. These coordinates, however, do not offer the complete formula for mixing the color because we still need to account for the presence of white or base color.

This diagram shows the color that is located at CMY coordinates {cyan 3, magenta 1, yellow 3}. The white cube is at {0, 0, 0}.

Calculating the Base Content

In the subtractive color space, white is referred to as the base color. Adding portions of primary colors to white reduces the amount of light reflected back to the viewer, resulting in the color becoming darker. Adding portions of white to any combination of primary colors increases the amount of light reflected back to the viewer, resulting in the color appearing lighter.

Each color within the COLORCUBE contains a measured quantity of white. This amount depends on the actual distance between the color and the white cube. All colors within the COLORCUBE contain an increasing proportion of white the closer they are to the white corner.

The diagram to the right illustrates the impact of white on a saturated hue.

See how the addition of yellow to white base changes the resulting color. Please note that the overall amount of paint remains constant.

To calculate the amount of white to add when mixing a color, first measure the distance between the selected color and the white cube. Do this by drawing a line from white to the outside edge of the COLORCUBE making sure the line passes through the color you are measuring.

Determine the amount of white in a color by measuring its distance from the white cube.

The relative distance from the color to the outside edge of the COLORCUBE defines the percentage amount of white in the mixed color.

Observe the progression from white to red as the percentage of base color decreases along the line above.

Simple Color Runs

To get a better understanding of how to use the colors, let us first look at the mixing instructions for colors on the outside edge of the cube. Here we look at the range of color between yellow and magenta.

Cyan Plane 0: Add yellow to white (across top). Add magenta to yellow (down left). Remove yellow (across bottom).

Starting at white, you can trace the progression of input primary colors as you move between the primaries yellow and magenta. Earlier we described the addition of yellow to white as seen across the top of the above face. As we move downwards towards red, yellow and cyan remain constant while magenta increases in value. Once red is achieved, we see magenta and yellow are at their full values. Now, as we move to the right, toward magenta, the amount of magenta and cyan remain constant, and the amount of yellow decreases.

To further illustrate this point, consider the mixing table provided below:

Starting at 100% yellow, add incremental amounts of magenta. After reaching red, reducing the amount of yellow in the mixture results in pure magenta.

The mixing instructions for each color are derived by first defining the positional information for that color. By recognizing that the COLORCUBE is divided into planes of primary color, then reading the positional information in terms of color planes, you can easily translate positional information into mixing information.

We will now discuss the third dimension of CMY color. The diagrams below depict how the run of colors shown above (white to yellow to red to magenta) changes with the addition of the third primary color, cyan.

These changes are illustrated graphically and in terms of paint strokes. See how mixing cyan with the original colors from cyan plane 0 changes their appearance. This progression is physically captured by the COLORCUBE as each of the colors move along the cyan axis.

Add cyan to each of the colors already discussed in order to enter the third dimension of paint color space.

"Cyan Planes 0 and 1": Move entire plane along cyan axis to achieve colors with 1 part cyan.

By continuing to add cyan to each of the resultant colors, you will soon reach the position defined by cyan plane 4. Note that the former color red will have progressed to black when the cyan content matches that of saturated magenta and yellow.

By first identifying a color based on its positional information within the COLORCUBE, you can then derive the proportions of primary and base color which you need to mix to get that color. This serves as a good starting point for mixing color. However, when mixing any color there will always be some variance from the exact mixing proportions, resulting in some variance in the color achieved. This brings us to final rule describing color mixing – color adjustments.

Once the color is mixed, you can fine-tune it by adjusting the proportions of primary and base color, moving it in one of eight directions within the color space.

To move a color progressively along a CMY axis, simply add more yellow, more magenta, or more cyan to it. Adding white will make the color lighter (closer to the white cube) and adding an equal proportion of all primaries will make the color darker (closer to the black cube). Recognizing the consequences of each of the additions will allow you better control when adjusting color combinations.

To move along a CMY axis in the opposite direction, you must remove a primary color. How to do this depends somewhat on what color is being modified. To reduce one of the four input colors, you must add more of the other three.

The procedure for mixing any particular color is as follows:

1. Locate the desired color within the COLORCUBE.
2. Identify the three planes that intersect the color.
3. Translate the point at the 3-plane intersection to mixing instructions. Plane 1 of yellow means one drop of yellow; plane 2 of yellow means two drops of yellow, etc. Do this for each of the three planes.
4. Draw a line from white through the color to the outside edge of the cube. The relative distance from the color to the outside edge of the cube defines the percentage amount of white to add. If the color contains 5 drops of primary color, and it lies one quarter the way from the closest outside edge of the cube, then the final mixture needs to contain 25% white (approximately 2 drops).
5. Adjust color as needed by adding or subtracting primary colors using COLORCUBE as a reference guide.

Removing Yellow

Adding cyan to green effectively "subtracts" yellow resulting in a color infinitesimally close to cyan. The same is achieved when cyan and magenta are added to black and when magenta and white are added to peach. Follow the lines below to see the progression of these operations.

Removing Cyan

Removing cyan from blue-violet is as simple as adding magenta. The result will eventually be a near-saturated magenta. To move from light purple to light pink, add magenta and white incrementally as in the diagrams.

Removing Magenta

To arrive at green from black, add yellow and cyan effectively removing magenta. As in the diagram below, add yellow to red to get orange/yellow and add white to magenta to get light pink.

The above examples illustrate removing yellow, cyan, or magenta from a color. As stated, "subtracting" a primary color is merely the addition of other primaries. Thus, the destination color results from the relative changes in the primary mixture.

Mid-gray plus or minus cyan, magenta or yellow content will move the color in some direction along the appropriate axis. The same holds true for black and white.

Maximizing the Color Space

The size of a color space gamut is most definitely a function of the three primaries that are used. If one or more of the primary colors are not pure, then the range of colors will be restricted. For example, a cube of paint constructed using the traditional painter primaries of red, yellow, and blue, will be ill -formed and irregular, as this combination of colors does not reproduce a full color gamut because of improper primaries. Remember, red can be made by mixing yellow and magenta; Painters’ blue can be made by adding magenta to cyan.

One of the best ways to test whether a color is primary is to use a prism. A separate document will explain this procedure in detail.

Conclusion

By modeling how the human eye sees color, the COLORCUBE represents a new way of teaching the principles of color. The concepts of color mixing, color naming and color visualization are all simplified by using a visible cubic color space. Mixing paint pigment is but one way to demonstrate the various uses of this three-dimensional model.

Learning to navigate about a color space is an intuitive skill that comes with a great deal of practice and experience. With an invaluable tool like the COLORCUBE, most color concepts become elementary.

The COLORCUBE also defines the model by which color is stored and manipulated within a computer. Becoming familiar with the color concepts embodied by the COLORCUBE makes understanding digital color technology easier, especially as color expertise relies on computer knowledge.

Finally, there is a color model that unites both the artist and the scientist. The COLORCUBE allows the language of color, as defined by artists, and the science of color, as defined by color theorists, to be understood by all individuals using a single model.