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May 1, 1997

COLOR NEWS TM

DIGITAL COLOR MODEL PUTS COLOR IN A NEW LIGHT Breakthroughs in color technology provide need for new model to represent and understand color.

By Ken Davies

More consumers than ever are buying digital imaging products. Digital cameras, color printers and color scanners have become less expensive and therefore, more accessible to new users. Accompanying this revolution in color usage is the need to understand digital color and its inherent complexity. Research indicates that typical end-users are baffled by the intricate behavior of color and often complain that “the colors that print do not match what is on the monitor”. In spite of astounding technological advances in color, it is readily apparent that few people understand the theory of how digital color works. This inability to fully comprehend new color technologies can lead to customer dissatisfaction and products that fall short of user expectations. Spittin' Image Software introduces a new “low-tech” invention designed to explain the principles of digital color. This recently U.S.-patented device, aptly named the COLORCUBE, serves as a physical model of how color is stored, manipulated,

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The COLORCUBE is a 3-dimensional model by which one can understand and teach digital color theory. This elegant representation of color bridges the gap between additive and subtractive systems of color, and defines the method by which colors are stored, manipulated, and reproduced using computer technology. SITE FOR SORE EYES

YOUR OWN COLORCUBE!!

Additional information on the COLORCUBE model and color theory is available on the Internet:

COLORCUBE kits feature: primary paints, prism, instruction manual and 11” COLORCUBE model.

www.colorcube.com

Contact Spittin' Image Software to order.

Copyright © 1997, Spittin’ Image Software Inc. # 102, 416 6th St. New Westminster, BC, Canada V3L 3B2 (604) 525-2170 www.colorcube.com

and reproduced using digital processes. Included with the COLORCUBE is a manual describing the 10 steps to understanding digital color. The following description is provided as an overview:

1

How the Human Eye sees Color

The eye contains two kinds of receptors: rods and cones. While the rods convey shades of gray, the cones allow the brain to perceive color hues. Of the three types of cones, the first is sensitive to red-orange light, the second to green light and the third to blue-violet light. When a single cone is stimulated, the brain perceives the corresponding color. That is, if our green cones are stimulated, we see “green”. Or if our red-orange cones are stimulated, we see “red”. If both our green and red-orange cones are simultaneously stimulated,

Spectral Sensitivity Curve for each of the cones in the human eye. our perception is yellow. The eye cannot differentiate between spectral yellow, and some combination of red and green. The same effect accounts for our perception of cyan, magenta, and the other in-between spectral colors. Because of this physiological response, the eye can be “fooled” into seeing the full range of

visible colors through the proportionate adjustment of just three colors: red, green and blue.

2

Identifying Primary Colors

Any color can be spectrally analyzed using a prism to determine its red, green and blue primary values (additive color

Viewing these circles through a prism isolates the primary colors. The circle on a white background breaks into Cyan/Magenta/Yellow primaries. The same circle on a black background breaks into Red/Green/Blue primaries.

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space), or its cyan, magenta and yellow primary values (subtractive color space). This simple yet powerful technique can be used to identify true primary colors. Choosing the correct three primaries maximizes the number of colors reproducible within a color space.

3

Additive and Subtractive Color

Televisions, cameras, scanners and computer monitors are based on the additive system of color (RGB), where red, green and blue light projected together yield white. Offset printing, digital printing, paints, plastics, fabric and photographic prints are based on the subtractive system of color (CMY/CMYK) in which cyan, magenta and yellow mix to form black (K). The unique feature of the COLORCUBE is that both systems are integrated within one model. Switching between RGB and CMY color systems is as simple as turning the model over.

4

Color Models

With each color theory advancement comes a new model by which to understand it. Unfortunately, users of older color technologies rarely, if ever, adopt these new models. For example, the color wheel is virtually identical in appearance and operation to how it was first conceived by Sir Isaac Newton. Painters continue to incorrectly define primary colors as red, yellow and blue according to the color wheel despite the fact that such technologies as offset printing and photography, each

RGB and CMY vertices, when placed in the same referential color space, form the outer dimensions of a cube. almost a century old, are based on a three-dimensional system of color using the true primaries cyan, magenta and yellow. Other models of color used by specialists in their respective vocations include: Hue/ Saturation/Value (HSV), CMYK charts, RGB Color Space, Pantone color system, CIE Color Space, DIN color chips and spectral luminance graphs. Computers and other digital devices define color based on a new model of color known as a COLORCUBE, which defines the digital representation of color.

5

Storing Images in Computers

All digital color devices that handle the storage, manipulation, and reproduction of color images do so by storing RGB values. Digitally storing an image requires that it first be broken

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down into a grid of tiny pixels (dots). Each pixel is sampled for the amount of red, green, and blue light present. The entire image is then stored one pixel at a time. To store a 3-inch square image at 150 dots per inch requires storing 202,500 pixels or 607,500 bytes. The theoretical model describing how colors are stored in a computer is often displayed as a cube. This method of storing color has proven to be remarkably adaptive, allowing conversions to a wide variety of color models; including the color wheel, CIE color space, HSV color, Munsell Sphere, Pantone system, DIN chips, and spectral definitions of color. The fundamental difference between the COLORCUBE and all other models of color is that it describes colors within a color space based on measured input quantities (what quantities of primary pigments are used to

make the color). Other models of color are based on measured output values (what the color looks like). Basing a color system on input values considerably simplifies issues related to color naming, color reproduction, color visualization, color calibration, color manipulation, and color mapping between color spaces.

6

Visualizing a Color Space

The ability to visualize all the available colors within a threedimensional color space and to see the inter-relationships between those colors is a huge advantage when working with color. Although there are a number of computer diagrams simulating a theoretical color space, the COLORCUBE model is the first of its kind to define a physical model with the interior colors visible. As the eye can see over 16 million colors, the key to the COLORCUBE concept is that the external edge points of the cube are defined, and interior colors then approximate the range of colors between end-

Color math in subtractive color space: 1) Equal amounts cyan, magenta and yellow (ABC) yield black (K). 2) Because of the following: • Equal amounts magenta and yellow yield red • Equal amounts cyan and yellow yield green • Equal amounts cyan and magenta yield blue 3) Color math can be used to determine that equal amounts red, green and blue also yield black. points. This then defines the outer dimensions of the visible color space, while allowing the viewer to see the internal elements. Color cubes of increasing density can then be generated based on a required “total” number of colors desired. A COLORCUBE that defines all colors reproducible within a color space would be 256 cubes on each side, for a total of 16,777,216 elements.

7

Color Mixing

Each color element within a COLORCUBE has a unique numeric identifier indicating what proportionate input values were used to reproduce the color. Each element also has a unique position within the cube, thereby ensuring that one can easily map between positional information and mixing information. If the mixing information is given, then the positional information can be deduced. If the positional information is given, then the mixing information can be deduced. This feature of the COLORCUBE eliminates much of the guess work associated with Planes of color in 3D color space

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naming, mixing, and describing a color, and ensures that within a defined color space, digital colors remain consistently reproducible.

8

Color Selection

The unique three-dimensional placement of colors within the COLORCUBE model works well as a color selection tool. Using the cube, it is easy to choose complementary colors, harmonious color runs, warm colors, cool colors, tints, shades, and colors of equal value. All color relationships can be shown to be mathematical in nature, and can be modeled using simple XYZ axis Cartesian math.

9

Color Manipulation

To manipulate colors within a color space one must first define a set of mathematical rules by which colors can be modified. Color Math, as it is referred to, relies upon first breaking colors into their constituent primary values, then doing the mathematical operation. The end

result is mixing instructions for a new color that can be found in the COLORCUBE. For example, to predict the result of adding two colors together, break down each color into its primary proportionate values. Then, add together the like primary values from both colors. The combined total for each primary yields the positional coordinates for the resulting color within the COLORCUBE. Similar logic can be applied to color subtraction (subtracting one color from the other), and to higher level operations such as adjusting contrast, brightness, and saturation.

10

Color Mapping and Calibration

The root of all color calibration and color mapping problems is that color spaces used by different color reproduction processes do not define the same visible area. Each color space is a subset of the true range of visible colors. To effectively map colors between different color spaces, a calculation must first be made to determine the color relationships between each of the color spaces. The objective when mapping

colors is to find the best approximation so that the final image does not appear blatantly altered. The current solution to correctly mapping colors between two color spaces requires spectrally analyzing the output characteristics of each device under controlled lighting conditions, and mapping the colors back to a CIE definition. Color mapping models in such popular software programs as Corel Photo Paint, and Hewlett Packard Scanning software, provide two-dimensional color calibration interfaces which are difficult to use, are incomplete, and require sophisticated knowledge about color. Software user interfaces that support color mapping could be vastly improved by recognizing the three-dimensional nature of color. Color space mappings could be visually represented in three-dimensional space relative to each other, and relative to the theoretical set of visible colors.

In Conclusion If a $50,000 digital color system does not perform to expectations,

the end user is likely to conclude they need more training. However, if a $5,000 digital color system does not perform to expectations, the end user is likely to conclude the product is broken. As digital color products become less expensive and sales volumes increase, the availability of economical product training will become an important issue. For users to understand how best to recognize and deal with complex color problems, they must become familiar with the fundamentals of digital color. The COLORCUBE is an elegant model of digital color which can be used to teach simple color concepts. Users can learn and properly understand the basic physiology of color perception, the intricate relationship between additive and subtractive color systems, and the mathematics of color image manipulation. At a time when art, science and other color-intensive industries are converging in the digital realm, a unified vision of color must emerge. The definitive model for that vision is the COLORCUBE.

References: 1.

The International Color Consortium. http://www.color.org

7.

True Internet Color. http://www.colorific.com/products/tic1.html

2.

Color Management: Current Practice and The Adoption of a New Standard. http://www.color.org/overview.html

8.

The Reproduction of Colour. Fourth edition. R.W.G. Hunt. Fountain Press, 1987.

9. 3.

QMS: Color Reproduction Basics. http://www.qms.com.www.products/color_paper/

The Color PC - Production Techniques. Marc D. Miller, Randy Zaucha. Haden Books, 1995.

4.

Is CIE L*a*b* Good Enough for Desktop Publishing? http://www.Is.com/cielab.html (defunct link)

5.

The Munsell System of Color Notation. http://munsell.com/munsell1.htm (defunct link)

6.

Through the 6x6x6 Color Cube - An Interactive Voyage. http://world.std.com/~wij/color/index.html

10. Color Science: Concepts and Methods, Quantitative Data and Formulae Gunter Wyszecki, W.S. Stiles. John Wiley & Sons Ltd., 1982. 11. Color Theory made easy. A new approach to color theory and how it applies… Jim Ames. Watson-Guptill, 1996. 12. Color Harmony 2. A guide to creative color combinations Bride M. Whelan. Rockport Publishers, 1994.

Copyright © 1997, Spittin’ Image Software Inc. # 102, 416 6th St. New Westminster, BC, Canada V3L 3B2 (604) 525-2170 www.colorcube.com

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The Color Math Concept The human eye is able to decipher patterns of light according to the primary colors of the additive system: red, green and blue (RGB). However, it is the subtractive system’s primaries: cyan, magenta and yellow (CMY) that best lend themselves to understanding the COLORCUBE and the concept of Color Math. This chapter unveils the inner workings of the COLORCUBE Model and the tools that are required for navigation in and about it. Within any given subtractive color space, as defined by the three primaries CMY, the use of Color Math will allow us to map the relationships of all the colors encompassed by that cubic area. Bridging the additive and subtractive systems of color, mixing colors, selecting color complements and converting color media equivalents all become matters of mathematics rather than that of guess work or compromise. Following a brief introduction to basic logic and scientific fundamentals, as they are relevant to color, we will expand upon the Color Math concept. By the conclusion of this chapter, we will be able to apply Color Math to a variety of tasks such as dissecting the COLORCUBE, dispelling critical aspects of traditional color theory, mixing colors, determining color complements and charting print-to-paint media conversions.

Principles of Color Math The similarity to commonly applied basics in mathematics and algebra will make these initial color principles appear somewhat elementary. However, their value will become apparent as the problems that we will encounter become increasingly complex. The diagram below illustrates the principle of symmetry that states that the order in which colors are added to one another does not alter the outcome. Figure 1. Color A + Color B = Color B + Color A

The addition (or subtraction) of two or more colors will likely cause a visible change in hue but we must also pay particular attention to the cumulative volume of the operation. For example, mixing one measurable unit of color with another yields twice the volume of the resulting color. The following diagram highlights this change in quantity using simple, like colors. Figure 2(a). 1 part Color A + 1 part Color A = 2 parts Color A

Also, this principle of cumulative volume applies to those operations involving varying colors as well. Figure 2(b). 1 Color A + 1 Color B = 2 Color C

As easy as these fundamentals are to grasp, the visual aids accompanying the upcoming problems shown may be counter-intuitive. The derivations of the Color Math “building blocks” presented in the next section will be the first step in making them fully comprehensible.

Primary colors We have stated that all of the colors captured within a color space are functions of the primaries cyan, magenta and yellow. The vertices or corner points on a COLORCUBE are these three pure hues (labeled A, B and C below), along with their various combinations. Together, these eight colors represent the key elements used in all Color Math calculations. Figure 3. Primary colors in the subtractive system

Although considered primary in the additive system of color, red, green and blue are the secondary colors in the subtractive system. By combining cyan with magenta, cyan with yellow and magenta with yellow, we are able to make blue, green and red respectively. As long as each primary ingredient is at full saturation and in equivalent quantities, the following operations hold true. Figure 4(a). 1 Cyan + 1 Magenta = 2 Blue

Figure 4(b). 1 Cyan + 1 Yellow = 2 Green

Figure 4(c). 1 Magenta + 1 Yellow = 2 Red

When all three primaries are mixed together in equal proportion, the resulting color is black. (editor’s note: this color mixture is mainly theoretical as we have yet to encounter perfect subtractive primaries that make a perfect black when mixed.) Figure 5. 1 Cyan + 1 Magenta + 1 Yellow = 3 Black

Black is also achieved when certain combinations of the primary and secondary elements are mixed. We recall from figure 4 (c), that red is made up of equal parts magenta and yellow. Therefore, we can add cyan to red in order to form black by virtue of the equation below: Figure 6. Color A + SUM Colors BC = Color ABC

And so, Figure 7(a). 1 part Cyan + 2 parts Red = 3 parts Black

Because each secondary color is merely a combination of two primaries, black is the result in each of the following mixtures. Please note the unequal quantities of the inputs and the constant amount of the sum. Figure 7(b). 1 Magenta + 2 Green = 3 Black

Figure 7(c). 1 Yellow + 2 Blue = 3 Black

The operations shown above may beg the question: what happens when the secondary colors are added together in equal quantities, as in the diagram below?

Figure 8. Red + Green + Blue?

Answering this question correctly requires a break down of each of the inputs into its’ constituent CMY elements in order to investigate the exact quantities being mixed. In order to simplify this task, we will take single units of red, green and blue and discover that they yield the following: Figure 9. Adding Red + Green + Blue (in terms of CMY)

Upon analyzing the CMY proportions in the sum, we recognize the color as black! This solution may strike you as odd. After all, if equal quantities of primary colors cyan, magenta and yellow make black, how can the same amounts of secondary colors red, green and blue possibly produce an identical result? Can the following diagram really be true? Figure 10. 1 Red + 1 Green + 1 Blue = 3 Black

The answer is “yes” because we have learned that, by definition; black is CMY in equal amounts at full saturation. (If the saturation or purity of the primary hues is less than full, some form of gray will emerge from the mixture. The value of the gray will depend on the amount of base color present.) So, in deconstructing red, green and blue into their respective CMY elements, we discover that these three colors cumulatively do indeed carry the correct CMY proportions to create black. Color Math will be used later in the chapter to prove the validity of this conclusion.

White as “Base” Color In the parentheses above, we alluded briefly to the concept of the base color. This is the color that is perceived when no primary hues are present. For instance, in color media that utilize the additive system of color, black is considered to be the base color. That is, the eye responds to the absence of red, green and blue (primaries in the additive system) and its perception is the color black. The opposite occurs in the subtractive system where zero values of cyan, magenta and yellow result in the perception of white. While the use of a non-white, non-black base is possible; the result is a truncated colorspace and a somewhat skewed COLORCUBE. Such is the case when looking through tinted eyewear or offset printing onto colored paper. Thus, in order to maximize the set of visible colors within our CMY color space, white will be the assumed base color. To this point in our discussion, all of the colors have been fully saturated containing no white or base color. We now attempt to understand the impact of the base color by infusing white base with increasing amounts of primary hues and observe the changes to the resulting color. Our analysis begins with total white base to which we add rising increments of yellow primary. As long as the overall volume of each color sample is held constant, the progression from 100% white leads to a fully saturated yellow. As the horizontal bars in the top left diagram show, the reduction of base color, white gives way to an increase of non-base content. The changes in the “base-to-primary” ratio results in graduated versions of a mixed color (known as tints due to the presence of white) as shown in the color circles. The upper right corner of the diagram below maps the same procedure using magenta primary. Figure 11. Adding primaries to a white base.

Let us now conduct a similar operation with two primary colors adding them both to the base color, white. We should recognize that the combination of equal parts yellow and magenta creates red but as illustrated above in the bottom left box, this mixture does not affect the proportion of the white base. The base color maintains its percentage value of 100, 75, 50, 25 and 0% of the total color respectively, regardless of the amounts of multiple primaries which make up the remainder. The same effect takes place when all three primaries are added to decreasing amounts of white base. As demonstrated in the bottom right corner above, grays and black are the result of mixing cyan, magenta and yellow with a white base. It is important to remember from these exercises that the CMY primary mixture occupies only the portion of the color that is non-base.

Constructing the COLORCUBE Returning momentarily to the progressions of magenta and yellow tints, we in fact derived two axes of the COLORCUBE. The plane of color, constructed in the figure 12, is what bridges the color space that exists between those two axes. Using a similar strategy to that exhibited earlier, we start with 100% white and incrementally reduce the amount of base color while increasing the primary content. The non-base portions of each color shown in the diagram are mixtures containing magenta and/or yellow. Horizontal bars once again capture the systematic increases in these mixtures within the fixed overall volume of color.

Figure 12. White-Yellow/Magenta plane

It should seem obvious that moving away from the white square horizontally implies a larger presence of yellow and likewise, a vertical movement downward results in the addition of magenta. What may not be so obvious is that these increases in primaries affect only the portion of color that is non-base. For instance, although magenta and yellow are maximized at a certain point in the “25% base color” diagram, they only contribute 37.5% each to the whole color. (In case this is unclear, the “certain point” that is being referred to is in the bottom left diagram, located in the middle of the color group and is the corner of the colored squares). The next diagram depicts the unified yellow-magenta plane previously constructed. The horizontal bars of color have been attached to their corresponding color to illustrate the proportions of base and non-base content in each. These “Color Bars” also make the pattern that exists between the relative quantities of the primaries themselves visually apparent.

Figure 13. Unified Yellow-Magenta plane

We will continue to attach these Color Bars to color samples in order to assist our understanding of how the COLORCUBE is built. They are graphic and mathematical representations of the ingredients present in each color and are standardized to a constant length for the purposes of measurement and comparison. The next phase of COLORCUBE construction involves the addition of the remaining primary, in this case, cyan. The above plane was theoretically conceptualized by taking the white-yellow axis and incrementally increasing magenta content while adjusting base content to maintain its proportion. This resulted in multiple axes containing various combinations of the white and primary colors. The incremental addition of cyan to this entire magenta-yellow plane will yield similar results in the form of multiple planes of color. This third dimension of color, as in the diagram below, is organized in terms of base color percentage (exactly as above) and each plane is separated according to cyan content. The Color Bars once again fix the overall volume of each color to a single value and allow us to see the actual color that each formula represents.

Figure 14. Increasing Cyan content incrementally

Applying Color Math Having completed our derivation of an entire COLORCUBE, we revisit the color theory basics from the beginning of the chapter and attempt to prove these operations using Color Math. In doing so we will introduce tools and techniques that will assist our understanding of CMY addition and subtraction as well as create a visual grounding to Color Math procedures.

Color Bars Horizontal bars of color were used extensively during the construction of the COLORCUBE to graphically depict the base and non-base content of each color they represented. They were extremely useful in allowing us to detect and map the patterns that exist within a color space. In this section these diagrams become accessories to the addition of color and precursors to actual Color Math.

Remembering that each Color Bar is standardized to a single set length, we are able to add these fixed amounts together in order to determine the configuration of their sum.

Figure 15

For example, a given quantity of 100% white plus an equal amount of 100% primary yellow would yield a color that is half base, half non-base with a 50% yellow hue. Figure 15 demonstrates this graphically. It shows that once the input colors are combined and the mixture is reset to the size standard of the original Color Bar(s), the resulting color is one that contains equal parts white base and yellow primary. Figure 16

The diagram to the left is another situation that involves base white. However, this example shows the second input to be a color containing unequal multiple primaries. When these Color Bars are added together we can see that the sum contains four parts base white to four parts non-base primary, which is made up of three parts magenta and one part yellow. Once this result is subsequently resized to the standardized length, we learn that the four white squares are proportionately equal to half of the resulting color. Likewise, the primaries magenta and yellow occupy 1.5 and .5 of the remaining units, respectively.

When adding colors using Color Bars, the presence of three primaries adds complexity to the equation but the procedure for solving it is the same. Figure 17 shows the summarization of three mixed colors. Each of the ingredients are gathered and grouped according their CMYW category. After this sorting process, these input values are sized down to the normal Color Bar in order to discover the formula of the resulting color. Grasping the need to calibrate all color combinations to a fixed amount is important because this normalization process allows us to estimate the colors with which we are dealing

Figure 17

Figure 18

using the cube diagrams in the previous section. Having become familiar with the patterns inherent to the COLORCUBE, we can navigate within that color space using the Color Bars as guides. Let us take for our next equation the sums of the last two operations and use them as inputs. After adding the Color Bars together, we can sort and recalibrate the sum to a fixed amount with all of the constituent elements intact. It should be clear by now that the usefulness of this “Color Bar” addition is severely compromised by the increasing complexity of the operations and a general inability to distinguish minute proportions with any degree of precision. Alleviating this requires a Color Math process that relies strictly on the objectivity of percentage values and quantities of color rather than that of a guessing science.

Color Boxes A method that addresses our need for exact numbers while retaining the benefits granted us by the Color Bars must begin with the information on hand being organized in a practical manner. The tables introduced here place the CMY formula of a color in a usable format that allows any color to be added and/or subtracted. It also takes into consideration the volume of color as well. Suppose we have three units of color gold (C20 M40 Y60) which is one of our inputs in a Color Math operation. Our first step is to determine its percentage base content by subtracting the CMY quantity that is greatest from 100. In this instance, yellow is most dominant with a value of 60. Consequently, this color contains 40% base white. The remaining 60% consists of primary colors cyan, magenta and yellow in relative proportion to the color’s CMY formula. Thus, we divide each of the primary quantities (20, 40, and 60) by the sum of those primaries (120) and multiply each by 60%. This yields adjusted weights of 10, 20 and 30% for CMY respectively. We find that this shade of gold is 10% cyan, 20% magenta, 30% yellow and 40% white. The table below summarizes this information as well as provides the volume calculation. Figure 19. Table for CMY breakdown

The next diagram displays the above information in a graphical format that actually maps the relative strength of each of the CMY element and places the overall proportion of the base color in the forefront. This Color Box format adds a visual dimension to the CMY formula and offers insight to the color itself.

Figure 20. Color Box

This Color Math documentation also makes use of tables and diagrams that isolate the current operation. These are fairly self-explanatory in that they summarize the actual quantities and volumes of color that are being added or subtracted in columnar form. In figure 21, “A” and “B” represent the input colors and “C” symbolizes the resultant color. Figure 21. Table of operation and accompanying graphic.

Introduction Complete At this point, the basics of Color Math have been fully explained. We pause here to welcome comments from you that either accept or reject the theories explored here. Please contact Spittin’ Image Software (604/525.2170 or [email protected]) for more information on Color Math and look for future developments on this fascinating subject on this website.

July 28, 1997

COLOR NEWS TM

MIXING IT UP WITH THE DIGITAL COLORCUBE MODEL COLORCUBE provides a simplified method and conceptual model for mixing colors as a way to understand digital color behavior.

By Ken Davies

A

B

C

D

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.

Visualizing the COLORCUBE in terms of “primary color planes” allows one to grasp the relationship between CMY input value coordinates and the perceived colors of a given color space. The above diagrams are various stages of progression from CMY content to full color. SITE FOR SORE EYES

YOUR OWN COLORCUBE!!

Additional information on the COLORCUBE model and digital color theory is available on the Internet:

COLORCUBE kits feature: primary paints, prism, color instruction manual and the COLORCUBE model.

www.colorcube.com

Contact Spittin' Image Software to order.

Copyright © 1997, Spittin’ Image Software Inc. # 102, 416 6th St. New Westminster, BC, Canada V3L 3B2 (604) 525-2170 www.colorcube.com

Introducing a Model 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 previous diagram 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.

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.

Base Content The following diagram illustrates the impact of white on a saturated hue.

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

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.

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}. -2-

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.

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

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.

Simple Color Runs

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

To get a better understanding of how to use the COLORCUBE to mix 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.

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

Measure the distance between given color and white cube to find the percentage of white.

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

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

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 quantity. 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.

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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.

Adding a 3rd Primary 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.

the exact mixing proportions, resulting in some variance in the color achieved. This brings us to final rule describing color mixing – color adjustments.

Color Adjustments

“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

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:

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

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. -4-

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 blueviolet is as simple as adding magenta. The result will eventually be a nearsaturated 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. The diagram to the right captures the essence of color adjustment. Navigating from a certain color will take place in one of eight directions. The COLORCUBE allows you to master color mixing by displaying the likely results of adding or subtracting each of the primaries. Middle 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. -5-

Maximize Color Space

Conclusion

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.

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.

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

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.

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.

The COLORCUBE also defines the model by which color is stored and manipulated within a computer. Becoming familiar

Copyright © 1997, Spittin’ Image Software Inc. # 102, 416 6th St. New Westminster, BC, Canada V3L 3B2 (604) 525-2170 www.colorcube.com

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The Color of Music Music, like color, is not easily categorized. Broad musical classifications including: Jazz, Blues, Rap, Classical, Heavy Metal, Celtic, Pop, Rock, Country, Easy Listening, Muzak, and so forth - provide only a simple description for a vast variety of expressionistic styles. Musical styles can also be associated with color, texture, and flavor. Think of the Blues, purple Jazz, white noise, and other descriptive attributes such as: dark, light, gray, raspy, sweet, sour, sharp, harmonious and disharmonious. Music can also be described in terms of melody, harmony, and rhythm, with different musical compositions placing different emphasis on each of the three musical elements. Coincidentally, color too can be described in terms of elements, or primaries, where the three primaries cyan, magenta, and yellow, mixed in combination with white define a visible color space. The COLORCUBE, a recent invention designed to help visualize color relationships within the three-dimensional color space, also can be used as a visualization tool in mapping the color of music. To understand this concept, first envision a cube made up of smaller cubes, each one a distinct color. Starting with white in one corner, there are three directions of movement within the cube. In the one direction you add cyan, in the other you add magenta, and the third direction you add yellow. In terms of geographic directions, as you move through the COLORCUBE away from white, you can either move north/south, east/west, or up/down. Any color within the COLORCUBE can now be defined as some unique combination of each of the three primaries. Light brown is 100% yellow, 50% cyan, and 25% magenta. Chromatic green is 100% yellow, 100% cyan, and 0% magenta. The absence of color is white. All three primaries in equal combination yield black. In other words, a particular color can be categorized by where it lies in the color space in relation to the other colors. Relating this back to music, if we were to map melody, rhythm and harmony onto cyan, magenta, and yellow within the COLORCUBE, we could then talk about music in terms of its color, and describe the relationship between different styles of music as differences in color within a three-dimensional framework. For example, sound without melody, harmony, or rhythm is known as white noise. Speech, or the sound of someone talking, takes on the equal attributes of melody, rhythm and harmony, and extends along the gray line within the interior of the COLORCUBE. Chimes, which are harmonious, without melody or rhythm, map to the color yellow. Classical music, with melody and harmony, but without the hard driving rhythm of rock, is appropriately green in color. Pop music, with lots of melody, but without complicated rhythm or harmony is cyan in color. A simple melody with hard driving rhythm gives you the Blues. Jazz, with lots of rhythm, some melody, and some harmony, is predominantly purple in color. Rap music, with lots of rhythm and some harmony, but little melody, is red in color. And finally, take a song with lots of rhythm, harmony and melody, and you've got Black Music, Man! This is not meant to infer that all Classical music is green, or that all Jazz is purple. Celtic music, for example, is a genre containing large differences in melodic, rhythmic and harmonic content. Mapping the various flavors of Celtic music to colors within a color space provides a second classification index indicating what type of music it is. Two different songs within a particular genre of music can then be compared as being ‘greener’, or ‘redder’ than the other, or being ‘too yellow’ or ‘too magenta’, or ‘too red’. Music, like color, if categorized in terms of melody, harmony, and rhythm, can be described in relation to other musical styles as differences in color by mapping it to a three dimensional structure based on color space. This method of categorization can be used to describe differences between music within, and between, various musical genres, in a way that enhances what is already intuitively understood by those who love and enjoy music. The COLORCUBE Puzzle is a patented invention, available exclusively from Spittin’ Image Software Inc. New Westminster, B.C. Canada. V3L 3B2. Tel: (604) 525-2170. Fax: (604) 520-0029. For more information about color and the COLORCUBE, visit www.colorcube.com. Copyright (c) 1998 Spittin’ Image Software Inc.

July 31, 1997

COLOR NEWS TM

COLOR MODEL TIMELINE GIVES BIRTH TO NEW GEM This collection of color models, compiled by F. Gerritsen, shows the extensive thought and theory that surrounds the phenomenon of color.

A) D)

By Winston Wong

Every revelation in color theory has brought about new models by which the perception of color can be understood and subsequently, taught. Whether driven by a new discovery or technological advance, each progression changes the way we think about color. This historical account of color is not unlike a “color model museum” where, like most concepts, significant changes in knowledge are recorded for posterity. The majority of these color models are thematic around basic geometric shapes. Circular models, which later become spherical, appear the most frequently and are very much in use today. Triangles are also used fairly extensively having evolved into intricate cones and pyramids. It is the square and cubic models, however, that draw an increasing amount of attention as a means of mapping out visual color spaces.

B) E)

C) F)

COLORCUBE

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Various models of significance: A) Newton’s color wheel – resulting from splitting white light into the colors of the rainbow. B) Munsell Sphere – a popular spherical model. C) Hickethier – the first known “cubic” model. D) CIE – model used by official international organization. E) Gerritsen – invented by the color theorist who compiled the models shown here. F) COLORCUBE - the latest step in color model technology.

Copyright © 1997, Spittin’ Image Software Inc. # 102, 416 6th St. New Westminster, BC, Canada V3L 3B2 (604) 525-2170 www.colorcube.com

Other models of significance in the diagrams are the Munsell Spheres and the CIE diagrams that, in their own rights, are the standards by which color is generally measured. For the purposes of teaching color especially with respect to color storage and manipulation within computer technology, the COLORCUBE model proves to be excellent. It is at once artistically simple and scientifically relevant. At last, there is a model that meets the needs of artists and scientists alike. We hope you enjoy seeing and contemplating how others have tried to understand color. This begs the question: what model best defines how you envision color?

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COLORCUBE Copyright © 1997, Spittin’ Image Software Inc. # 102, 416 6th St. New Westminster, BC, Canada V3L 3B2 (604) 525-2170 www.colorcube.com

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1997