ArtColors:

ArtColors provides intuitive color mixing in subtractive Red-Yellow-Blue color space. It's a digital version of the traditional art school color wheel, which provides triadic, split-complementary,tetradic and analogous color harmonies. It helps to select pleasing palettes of colors. ArtColors also provides RGB-to-RYB conversion with simple formulas. The program is built with RayLib and RayGui, but the RYB-RGB formulas can be used separately in your own code.

First beta release: March 2020. Version 0.20 released in April 2021. See Roadmap.md and Changelog for details.

Goals

1. Intuitive color mixing for graphic design, data visualization, GUI creation or video game graphics.

   Everyone grows up learning that yellow and blue make green, not cyan! Additive mixing in the RGB space is unintuitive. Subtractive mixing in the RYB space is familiar.

2. Easy generation of harmonious palettes for pleasing graphic design.

   The basic color schemes in fine art are based on simple geometric relations on an RYB color wheel which has red, yellow and blue primaries 120 degrees apart. The typical RGB color wheel has red, green and blue 120 degrees apart, so these relations fail. In RGB, the blue-green spectrum tends to dominate, obscuring yellows, purples and browns.

3. Portable simple formulas for RYB-to-RGB conversion and subtractive color mixing.

   There is a lot of literature on subtractive color mixing. My approach aims for a compromise between simplicity and accuracy, with much less code than a reflectance-based approach. Most subtractive color mixing is done in the CMYK- space, rather than RYB, so hopefully these formulas fill a need.

How To Use ArtColors

To pick a color palette

Select a type of color palette (triadic, tetradic, etc.) by clicking on the Palette Type button, then rotate the Hue slider. The small squares that move around the perimeter of the wheel indicate the principal colors of your palette. They are the same colors as shown in the larger rectangles to the right of the wheel, which also show their RGB values. The swatches to the right vary the hue and saturation of your principal colors to provide a wide range of options. You can export these values to disk by pressing the "Save swatches to .pal" button. Done!

You may also wish to check whether your palette is suitable for colorblind users. In the lower right, clicking the "Colorblind mode" button changes your color swatches to approximate how they may be perceived by viewers with various color vision deficiencies: protanopia, deuteranopia, tritanopia and achromatopsia. Click once more to return to normal view. A colorblindness check is especially important for data visualization.

To mix your own shades using RYB

On the lower left of the screen, there are two areas to generate colors from RYB values using sliders for Red, Yellow and Blue values. These colors, or any other colors on the screen, can be blended by sampling them. Click "Pick Color" and left-click on one color, then click "Pick Color" again and right-click on another color. They will appear on the left and right sides of the color mixing bars in the middle-right of the screen. The subtractive color mixing bar uses our algorithm to represent better how pigments blend in art media (paints, inks, pencils, crayons).

Explanation of the Interface

Canvas Color - Switches between black or white background. You should definitely view your colors against both backgrounds, especially to appraise very light tints or dark shades.

Palette Type - Choose from one of six types of color harmonies (see explanation below). The harmonies have different numbers of principal colors: Triadic has 3, Split Complementary has 3, Square Tetradic has 4, Rectangular Tetradic has 4, Complementary just 2, and Analogous has 4. Your basic theme colors are those which appear to the right of the color wheel, and their locations are marked by small squares, similar to the windows in a handheld color wheel (see picture below).

Palette Swatches - Determined by your selected palette type. A range of saturations and tints/shades based on the theme colors, from almost-black to almost-white, and from low saturation to high.

Custom Color Mixing - At the bottom of the screen are two Red-Yellow-Blue mixing areas. Color A and Color B are mixed in the color mixing bars according to three kinds of mixing (see explanation below): Additive Quadratic mixing, Additive Linear mixing (the one you are used to), and Subtractive (yay!). Check the tiny box above "Inverse" to display the inverse color of the subtractive mix. Each color bar starts from 100% of Color A to 100% of Color B, ranging by 10% steps in between.

All Color Triplets shown on-screen are RGB values so you can copy them down if you'd like.

Exporting - Palettes are saved in .pal files, which are an ASCII readable standard. You can import the palettes into GIMP, Paint Shop Pro, Adobe, etc. Save swatches will save all the color swatches. This will be 72 times the number of theme colors in your palette. Save color bars will save the color mixing bar of your choice. Color bar palettes are only 11 colors in size. If you check the "Inverse" box, an option to save the inverse color bar will also appear.

If you want to extract the RGB data from the .pal file with a text editor, the first three lines of the file are: a FOURCC code (JASC-PAL), a file type version (100) and the number of colors in the palette. All subsequent numbers are RGB triplets for each color in the palette. Lines are terminated with \r\n. The file can safely be edited to suit your needs. Some programs may require either 16 or 256 colors in a .pal file; others don't abide by this convention, including GIMP.

Screen Shot - Useful if you want to import the whole screen into a graphics program, and sample there whatever hue you want.

Challenges and Design Principles of ArtColors

A brief summary of the challenges of designing a subtractive Red-Yellow-Blue color space explains the principles I used to design ArtColors. It also summarizes many of the things I learned while researching this project, and so I offer it in case it is instructive to others.

Hereafter common color space names will be abbreviated as follows:

RYB-=Subtractive Red-Yellow-Blue color space Our color system.
RGB+=Additive Red-Green-Blue The system most widely used for monitor display. Wiki
HSV=Hue-Saturation-Value An alternative representation of the RGB+ system. Wiki
CYMK-=Cyan-Yellow-Magenta-Black A subtractive system, most frequently used in printing. Wiki

Challenge #1: Everyone learns color mixing using RYB- primaries not RGB+

From the time you first played with crayons or fingerpaints, you've been using an RYB- color space. Red plus green make a murky brown, but in RGB+ they make yellow. Red and blue make a dark purple, but in RGB+ they make a bright magenta. This can make it hard to quickly find the colors you want when blending.

RGB+ makes sense for what it was designed to do. Computer monitors are emissive: they emit light which therefore blends additively. No painting can do this. Art media are reflective: the pigments we use absorb incident white light and reflect what they don't absorb. Thus, they are subtractive: the more pigments one adds, the less light is reflected to the eye. RGB+ was designed to align two of its primaries (blue and green) with two of the colors of light to which the three types of human cone cells in the eye are most responsive. RGB's third color, red, was chosen instead of the third cone color of yellow-green to give breadth of palette for mixing and the particular red was somewhat based on available emissive light sources at the time.¹

Some disadvantage of RGB+ are: the vast majority our experience mixing colors is in a subtractive space, and many colors in our experience are non-spectral (see below).

Moreover, traditional instruction in fine art still uses RYB- to teach color theory, as well as some textbooks in practical and decorative arts.² Traditional art color theory has a long and complex history, in part driven by the range of pigments available to artists and their vast experience. While the theoretical formalization of this body of knowledge into RYB- was premised in part (but only in part!) on erroneous 19th century ideas of the physics of color, the approach is still fundamentally valid -- as evidenced by the fact that artists, who devote enormous study to color -- still use it as a reference today. The success of RYB- does not depend on its ability to theoretically unify the physics of light and human physiology, but on its empirical validity to accurately predict what color will result from subtractive color mixing.³

Thus almost everyone who has ever taken an art class or read a book on art color theory has encountered the standard RYB- color wheel:

Principle #1: ArtColors should mimic a standard RYB- color wheel

Challenge #2: RGB+ and HSV color wheels are blue-green dominated

Because two of the three primaries are green and blue, the yellow-orange range is severely compressed, purple is likewise narrow and dominated by magenta. One has to be sniper to select these hues. Small changes in RGB values or HSV hue quickly sweep through these ranges of color.

Compare the standard HSV color wheel with the ArtColor color wheel to see the problem and its solution:

Principle #2: ArtColors should make it easy to select a wide range of hues by balancing the spectrum

The ArtColor Wheel broadens the yellow-orange spectrum and adds deeper purples, while keeping distinct lines for cyan and magenta. Note that red, yellow and blue primaries (small squares) are separated by 120 degrees. This will faciliate traditional palette selection and blending (see below). How to transform RGB+ to RYB- is where the math gets interesting.

If you are the inquisitive sort who wonders why RGB+ fails at providing a balanced spectrum of colors, there are two reasons. The first we can summarize by analogy: green and blue aren't very "orthogonal" in our color experience. But this merely begs the question: why not? The answer is not trivial. Indeed the question is even more perplexing when one considers that RGB is based in part on the physiology of human cone cells. Shouldn't green and blue seem orthogonal to us insofar as they are aligned to the "vector bases" of our separate cone cell "inputs"? The answer is that our psychological perception of color is not a direct result of human cone cell neuron response curves. The brain does its own mixing to create colors we commonly experience but are not aligned to the frequency-response curve of any one cone cell. Read about the Ewald Hering's opponent process theory of vision or the excellent overview in Clive Maxfield's article for details. Second, there are non-spectral colors: you don't see them in prismatically separated light.

Non-spectral colors include:

• All grays! (thank you, rod cells)
• All tints and shades = art terms for adding white or black respectively to a "pure" color. All mixtures of a spectral color plus any shade of gray (from white to black) result in a non-spectral color. In physical media, this happens all the time!
• Important hues like purple or brown (and any tint or shade thereof, like pink or rose). "Purple" isn't a spectral color: the perception of purple is the psychological result when the brain receives stimuli from both the red-sensitive and blue-sensitive cone cells at the same time.

So RGB is based on the physics of emitted light, and its primaries are selected (partly) based on the physiology of human cone cells. But RGB doesn't factor in higher-level yet intrinsically human neurological factors of how the brain generates certain color perceptions that are non-spectral. Art color theory was attentive to this fact from mere experience, even without understanding of the underlying causes. In this regard, they were better empiricists, and RYB- theory reflects that advantage in my opinion.

Challenge #3: Preserve traditional color harmonies in palette selection

The term color harmony is used in art to describe the theory of choosing attractive palettes which achieve different artistic effects. In a musical harmony, notes played at the same time need to be sufficiently distinct to avoid dissonance, but the separation between the notes achieves the overall feeling of the chord (major chord vs. minor, etc.). So likewise in a color harmony, colors are chosen that pair together to achieve a palette that produces a certain aesthetic effect. (A bonus for color harmonization, unlike music, is that a narrow range of colors (called analogous) are not dissonant.) A "complementary color" is its "opposite" on the traditional color wheel, which has its roots in the after-image one sees after looking at a bright color then looking at white.

A book on color theory for painting will effectively demonstrate how a painter's choice of palette greatly impacts his artwork.

On a traditional artist's color wheel, the theory of color harmonies is neatly summarized by the geometrical relationships seen in the central circle of the wheel:

The traditional palette schemes and their geometries in RYB color space are:

• Triadic

  Colors separated by 120 degrees

• Split Complementary

  Two other colors offset by 30 degrees from the complementary color of the first.

• Square Tetradic

  Colors at 0, 90, 180, 270 degrees. Two sets of complementary colors, separated by 90 degrees.

• Rectangular Tetradic

  Colors at 0, 120, 180, 300 degrees. Pick two complementary colors. For each, find their two triadic harmony colors and make these four a set. These latter four colors make up the rectangular tetradic scheme.

The problem: These geometrical relations depend on RYB primaries separated by 120 degrees, which RGB does not provide. Thus an RGB or HSV color wheel makes it difficult to select traditional harmonious palettes because green, not yellow, is 120 degrees from red and blue. Even some sophisticated online color pickers claim to provide these color harmonies, but they fail because they use the correct degrees of separation, but the wrong basis (HSV), yielding incorrect colors.

Principle #3: ArtColors should provide traditional color harmony palettes using the above geometrical relationships on an RYB color wheel.

Harmonious palette selection should be as easy as rotating the Artist's color wheel. Pick one color, and the others are automatically selected. A palette using these hues, their tints, shades and mixtures, can then be automatically exported. Export can include something simple as invoking a function with one color as input, and returning an array of harmonious colors.

Challenge #4: RGB to RYB translation

There is a lot of literature on the standard color spaces (RGB, HSV, CMYK, CIELAB, etc.) and the mapping functions between them have all been nicely defined. There is much less written on RGB to RYB translation and RYB (to my knowledge) does not have a standardized colorspace devoted to it!

RGB to RYB

The ArtColor algorithm for translating from RGB to RYB uses trilinear interpolation. First, construct a cube. The bottom left corner is black. Each dimension is associated with a primary color in RYB space. Thus, the bottom right front vertex represents peak red value and the x-axis the range of reds. The top left front vertex is yellow, with the y-axis representing the yellow range. The botton left back vertex is blue, with the z-axis representing the blue range. The vertex diagonally opposite black is white. The remaining vertices correspond to the secondary RYB colors obtained when mixing our primaries: green (=blue+yellow), orange (red+green) and purple (red+blue).

We then assign RGB values to each of these RYB vertices. We can thus translate every color in the RYB space to RGB by a trilinear interpolation, following the useful paper by Gosset and Chen.⁴ A picture is worth a thousand words here:

In the code itself, we use normalized float values (0.0 to 1.0) for our coordinates rather than 8-bit integer triplets (0-255,0-255,0-255) to avoid rounding error in our functions. We translate back to 8-bit integers at the end for RGB display.

While RYB red is defined as (255,0,0), the choice of RGB value for RYB blue and yellow is not straightforward. Choosing RGB (0,0,255) for blue initially seems obvious, but our primary color values must be chosen to facilitate a range of hues around our RYB color wheel. We are, in effect, compressing the very broad RGB green-blue range to expand the yellow-orange range (and the purple range to a lesser degree). Choosing RGB values for blue and green that are too intense will result in little hue variance around these two points on the color wheel, resulting in "flat spots" in our spectrum. To give a richer spectrum of hues, different values were chosen, using a slightly darker green and slightly brighter blue. Here is an example of the problem:

Choosing RGB values for Blue and Green which optimize the whole spectrum is also important for the generation of color harmony palettes. "Flat spots" in the spectrum result in hues which don't vary smoothly as the other colors in the palette vary, resulting in similar blues and greens for palettes which should be different.

There is no single "canonical" way to assign RGB values to our RYB space. To my knowledge, there's never been a standard for RYB-. As such, I exercised my judgment using reference colors from sites which give RGB equivalents to oil/acrylic paint hues as a guide. The same goes for assigning RGB values to the RYB secondary colors of orange and purple. I tried to keep these values close to art colors which use these hue names, although there is variation in what is considered "ideal" orange and "ideal" purple. I aimed to keep purple distinct from magenta (which is more red than blue) and a "middle of the road" orange between red and yellow. The only choices which are indisputable was assigning Black=RGB(0,0,0) and White=RGB(255,255,255). A different red could have been chosen, but since red is not in the "problematic" green-blue range, full RGB(255,0,0) red seemed to work very well.

RYB to RGB (Inverse function)

The RYB-to-RGB function also uses a trilinear interpolation. Creating this inverse function was not straightforward. I need to see if I can disentangle everything algebraically and find an analytical inverse. But in the meantime, I started with an estimate for the corner values and then used a calculus-of-variations approach and a separate program to tweak the corner values such that an RGB-to-RYB-back-to-RGB tranformation produced close to the original color. If you uncomment the relevant bit of source code, you can get a comparison of the results. It's not bad but also not great -- nearly perfect in some spots and a bit off in others. So conversions back-and-forth between the two colorspaces using these formulae will introduce some corruption of hue.

Challenge #5: Subtractive Color Mixing

The paint and dye industry has figured out this problem. The best solution to replicating subtractive color mixing in an RGB+ display involves calculating the reflectance spectrum of each component pigment: the amount of light reflected for every wavelength in the visible spectrum measured in 10nm increments. Then this data is stored in a table. (Some tables for sRGB colors also exist.) Then one of several algorithms, often iterative for accuracy, are used to blend these reflectances and produce an RGB color. This is the "right" way to do it. The results are excellent.

It is also the cumbersome way. For a graphics artist who is not trying to exactly replicate real-world pigments but who just wants to subtractively and intuitively mix colors, something far simpler should do. Short formulas on StackExchange often give poor results ⁵, although some software packages provide this functionality effectively, like Krita painterly mixer using the Kubelka-Munk algorithm. But this algorithm is still fairly complex.

Principle #5

ArtColors should provide a simple function call that subtractively mixes two colors in a realistic way with a minimum of code, taking only two RGB inputs and a blending ratio, like this: Return Color=SubtractiveMix(Color a, Color b, percentage)

ArtColors uses an algorithm which (I think) gives pretty good results with a fraction of the code of the other methods, and no need for calculating or storing reflectance data or computationally complex formulas. The goal is 80% realism with only 20% of the code.

The basic approach was inspired by considering how paints actually mix. Examine this close-up of paints mixing:

If you look carefully, you can see that in some areas, the two paints are completely blended, and the result is subtractive: yellow and blue are making a much darker green. Red and blue are making a very dark purple. Yet in other areas, where the blending is not so thorough, fine lines of yellow and blue exist side-by-side. These paints are reflecting yellow and blue light. At a distance, these colors are additively blended by the eye when the distict swirls are too small to be seen.

Consider further that mixing paints is a mixture in the Chemistry sense: no chemical change happens. The red and blue molecules are still there in the thorough blend, doing exactly what they were doing when separate: reflecting red and blue light. There's just a lot of subsurface physical effects going on as light bounces around in the medium. Incident light is absorbed and reflected by one molecule, and then by another, and eventually the result reflects out to the eye.

How does this help solve our problem?

Strictly subtractive approaches start with White, and then subtract the RGB values of Color A and Color B from White, and return what is left. This approach is often too dark. Why? Some of each pigment is still reflecting its distinctive color on a tiny scale. If we take an approach that is part additive, part subtractive, we get a more realistic result!

Moreover, if Color A = Color B, our function should return that same color. Mixing the same color with the same color should equal the same color! Using a strictly subtractive algorithm, the result is a darker version of the original hue (because the input color values are subtracted from White twice). The closer the two input colors, the less change should be seen in the blend.

The ArtColor code for subtractive mixing is:

Color ColorMixSub(Color a, Color b, float blend) {
    Color out;
    Color c,d,f;

    c=ColorInv(a);
    d=ColorInv(b);

    f.r=max(0,255-c.r-d.r);
    f.g=max(0,255-c.g-d.g);
    f.b=max(0,255-c.b-d.b);

    float cd=ColorDistance(a,b);
    cd=4.0*blend*(1.0-blend)*cd;
    out=ColorMixLin(ColorMixLin(a,b,blend),f,cd);

    out.a=255;
return out;
}

Explanation of Code: Color a and Color b are the input colors. blend specifies how much of each color to blend, from 0 to 1.0, like a linear interpolation (LERP). 0.0 = All color A, 1.0 = All color B. 0.5 = 50%-50% mix of A and B.

First we find the RGB inverses of Color a and b, and assign them to new colors c and d.

    c=ColorInv(a);
    d=ColorInv(b);

Then we subtract both c and d from pure RGB White, clamping the result to zero, and assign the result to color f.

    f.r=max(0,255-c.r-d.r);
    f.g=max(0,255-c.g-d.g);
    f.b=max(0,255-c.b-d.b);

So far, f is the purely subtractive result, which suffers from the problems mentioned above.

Next, we calculate the "Color Distance" between Color a and Color b, which is just the vector distance between them in RGB space, normalized between 0.0 (identical colors) and 1.0 (completely opposite, like white and black).

float cd=ColorDistance(a,b);

This value will help solve the problem that mixing two similar hues should not change the result very much. The color distance factor cd is then tranformed by a quadratic transfer function, which regulates how much subtractive and additive mixing we do:

cd=4.0*blend*(1.0-blend)*cd;

The endpoints ensure that blend percentages near 0% or 100% look very close to the original input colors. The quadratic curve gives a good color gamut for the mix that comes next. The peak of the curve is determined by color distance. The output of this function determines the amount of additive vs. subtractive blending in our result. More distant colors will blend with a more subtractive dynamic (fully subtractive at y=1.0). Similar colors blend with a more additive dynamic (a flatter curve) that still has a subtractive factor. The maximum of the quadratic transfer function is the normalized color distance, so colors diametrically opposed in the color space will blend fully subtractively.

The last line does all the work:

out=ColorMixLin(ColorMixLin(a,b,blend),f,cd);`

First, we additively mix Color A and Color B in the specified blend ratio, which is accomplished by ColorMixLin(a,b,blend). This represents the additive blending effect of those fine swirls of color in the image above and subsurface interaction. Absence of this factor may be where a strictly subtractive approach yields odd results. This additive result is then blended with our purely subtractive result color f, according to the transfer function mentioned above, which is based on the color distance between Color a and Color b.

Voila! A pretty good result occurs for a wide range of input colors. Examples are below.

ArtColors provides two different kinds of additive mixing

Someone on StackOverflow kindly shared that the range of RGB values (0-255) came from the square root of camera CCD intensity signals, so the usual linear interpolation of RGB values actually darkens the result somewhat.

Therefore ArtColors provides two kinds of additive mixing.

Linear Additive Mix -- the formula used everywhere:

Color ColorMixLin(Color a, Color b, float blend) {
    Color out;
    out.r=(1.0-blend)*a.r+blend*b.r;
    out.g=(1.0-blend)*a.g+blend*b.g;
    out.b=(1.0-blend)*a.b+blend*b.b;
    out.a=(1.0-blend)*a.a+blend*b.a;

return out;
}

Quadratic Additive Mix -- we square the RGB values, LERP those, and square root the result. This mix tends to preserve brightness / intensity somewhat better because the square of the RGB value is what actually corresponds to light intensity.

Color ColorMix(Color a, Color b, float blend) {
    Color out;
    out.r=sqrt((1.0-blend)*(a.r*a.r)+blend*(b.r*b.r));
    out.g=sqrt((1.0-blend)*(a.g*a.g)+blend*(b.g*b.g));
    out.b=sqrt((1.0-blend)*(a.b*a.b)+blend*(b.b*b.b));
    out.a=(1.0-blend)*a.a+blend*b.a;

return out;
}

ArtColors provides all three mixes (Quad Additive, Linear Additive, and Subtractive) for any two input colors, blended in 10% intervals. The top color bar is Quad Additive, the middle is Linear Additive, and the bottom is Subtractive Mixing in the examples below:

Red and Blue make a dark, rich Purple.

The relatively opposed colors in this triadic palette of Mint-Magenta-Gold blend darker:

Blending three primaries should result in brown -- and it does!
(Red+Yellow gives the Orange on the right, Blue is on the left.)

Blending two similar colors, like this Vermillion and Orange, should yield results quite close to our inputs. Yet close inspection of the RGB values of the three color bars shows that quadratic additive is lighter than linear additive, which is lighter than the subtractive mix.

Footnotes

1. Blue and Green had the double merit of aligning with human physiology (cone cells) and practical production. RGB Red, however, lacked physiological foundation and so its value was struck as a compromise: it happened to align with a red line in the spectrum of mercury discharge bulbs at the time, but it was also in a range of color where the human eye's response was rather dull to subtle variations of hue, so it provided a "slop factor" for the foreseeable future when mercury discharge lighting would be replaced by some other form. See the article on the CIE 1931 RGB colorspace for details. RGB was further reinforced by the three phosphor colors of old-fashioned color TV sets, with an acceptable red once again being the most difficult phosphor to obtain.

2. Consider Albert O. Halse's book for students of interior design, The Use of Color in Interiors. The first chapter is devoted to basic color theory, which begins with the obligatory mentions of the contributions of Goethe and Newton. Several pages are devoted to the Ostwald color system and the Munsell color system. The CIE colorspace is mentioned, and the entire subsequent chapter is devoted to the effect of various lamps on color, where CIE has also made considerable contributions. He also reviews briefly the ambitious Universal Color Language project of the Inter-Society Color Council. After all these systems have been introduced to the student, we read: "One simple and useful system is the chromatic circle, which uses red, yellow, and blue as its 'primary' colors. While not in agreement with the physicists, it is very satisfactory for use by architects an interior designers" (p.13). The balance of the chapter discusses how the traditional analogous, complementary, triadic, etc. palettes may be devloped for architectural and interior design proposals. Halse's chromatic circle is the same as we use here, with RYB primaries at 120 degrees and palettes described on the basis of this arrangement. Albert O. Halse, The Use of Color in Interiors, Second Edition (New York: McGraw-Hill, 1978).

3. There is a physiological basis to the traditional color wheel which relates it to both common experience and the later science of how our neurons work. Opposed colors on the wheel (i.e, separated by 180 degrees) are so arranged because if you stare at one for a long time, then look at a white page, the after-image you see is the opposed color.

4. http://vis.computer.org/vis2004/DVD/infovis/papers/gossett.pdf

5. https://stackoverflow.com/questions/1351442/is-there-an-algorithm-for-color-mixing-that-works-like-mixing-real-colors