Painters long mixed colors by combining relatively bright pigments with black and white. Mixtures with white are called tints, mixtures with black are called shades, and mixtures with both are called tones. See Tints and shades.[1]
Optimal color solid plotted within the CIE L* u* v* color space, with D65white point. Because it is (approximately) perceptually uniform, it has an irregular, not spherical shape. Notice that it has two sharp edges, one with warm colors, and the other one with cold colors.
Different color theorists have each designed unique color solids. Many are in the shape of a sphere, whereas others are warped three-dimensional ellipsoid figures—these variations being designed to express some aspect of the relationship of the colors more clearly. The color spheres conceived by Phillip Otto Runge and Johannes Itten are typical examples and prototypes for many other color solid schematics.[2]
As in the color wheel, contrasting (or complementary) hues are located opposite each other in most color solids. Moving toward the central axis, colors become less and less saturated, until all colors meet at the central axis as a neutral gray. Moving vertically in the color solid, colors become lighter (toward the top) and darker (toward the bottom). At the upper pole, all hues meet in white; at the bottom pole, all hues meet in black.
The vertical axis of the color solid, then, is gray all along its length, varying from black at the bottom to white at the top, it is a grayscale. All pure (saturated) hues are located on the surface of the solid, varying from light to dark down the color solid. All colors that are desaturated in any degree (that is, that they can be though of containing both black and white in varying amounts) comprise the solid's interior, likewise varying in brightness from top to bottom.
Exterior view of color sphere of Albert Henry Munsell, 1900. This is actually a drawing of a physical model that was manufactured and sold.
Interior cross section of Munsell's color sphere and color tree, 1915. Munsell was the first known person that separated hue, value, and chroma into perceptually uniform and independent dimensions, and he was the first to illustrate the colors systematically in three-dimensional space.[3]
Philipp Otto Runge’s Farbenkugel (color sphere), 1810, showing the surface of the sphere (top two images), and horizontal and vertical cross sections (bottom two images).
Color sphere of Johannes Itten, 1919–20. A much clearer representation of his model appears in The Art of Color, 1961, which cannot be reproduced here for copyright reasons.
Color sphere modeled in salt dough by Jesse Hensel, 2011.
Section of Hensel's sphere revealing some of the desaturated colors.
Optimal color solid
The optimal color solid or Rösch–MacAdam color solid is a type of color solid that contains all the possible colors that surfaces can have. That is, the optimal color solid is the theoretical limit for the color of objects. It is bounded by the set of all optimal colors.[4]
The reflectance spectrum of a color is the amount of light of each wavelength that it reflects, in proportion to a given maximum, which has the value of 1 (100%). If the reflectance spectrum of a color is 0 (0%) or 1 (100%) across the entire visible spectrum, and it has no more than two transitions between 0 and 1, or 1 and 0, then it is an optimal color. With the current state of technology, we are unable to produce any material or pigment with these properties.[5]
Thus four types of "optimal color" spectra are possible:
The transition goes from zero at both ends of the spectrum to one in the middle, as shown in the image at right.
It goes from one at the ends to zero in the middle.
It goes from 1 at the start of the visible spectrum to 0 in some point in the middle until its end.
It goes from 0 at the start of the visible spectrum to 1 at some point in the middle until its end.
The first type produces colors that are similar to the spectral colors and follow roughly the horseshoe-shaped portion of the CIE xy chromaticity diagram (the spectral locus), but are generally more chromatic, although less spectrally pure. The second type produces colors that are similar to (but, in surfaces, more chromatic and less spectrally pure than) the colors on the straight line in the CIE xy chromaticity diagram (the line of purples), leading to magenta or purple-like colors.
Spectrum of a color-optimal reflective material. There is no known material with these properties, they are, for what we know, only theoretical.
In optimal color solids, the colors of the visible spectrum are theoretically black, because their reflectance spectrum is 1 (100%) in only one wavelength, and 0 in all of the other infinite visible wavelengths that there are, meaning that they have a lightness of 0 with respect to white, and will also have 0 chroma, but, of course, 100% of spectral purity. In short: In optimal color solids, spectral colors are equivalent to black (0 lightness, 0 chroma), but have full spectral purity (they are located in the horseshoe-shaped spectral locus of the chromaticiy diagram).[6]
In linear color spaces that contain all colors visible by humans, such as LMS or CIE 1931 XYZ, the set of half-lines that start at the origin (black, (0, 0, 0)) and pass through all the points that represent the colors of the visible spectrum, and the portion of a plane that passes through the violet half-line and the red half-line (both ends of the visible spectrum), generate the "spectrum cone". The black point (coordinates (0, 0, 0)) of the optimal color solid (and only the black point) is tangent to the "spectrum cone", and the white point ((1, 1, 1)) (only the white point) is tangent to the "inverted spectrum cone", with the "inverted spectrum cone" being symmetrical to the "spectrum cone" with respect to the middle gray point ((0.5, 0.5, 0.5)). This means that, in linear color spaces, the optimal color solid is centrally symmetric.[6]
In most color spaces, the surface of the optimal color solid is smooth, except for two points (black and white); and two sharp edges: the "warm" edge, which goes from black, to red, to orange, to yellow, to white; and the "cold" edge, which goes from black, to blue, to cyan, to white. This is due to the following: If the portion of the reflectance spectrum of a color is spectral red (which is located at one end of the spectrum), it will be seen as black. If the size of the portion of total or reflectance is increased, now covering from the red end of the spectrum to the yellow wavelengths, it will be seen as red. If the portion is expanded even more, covering the green wavelengths, it will be seen as orange or yellow. If it is expanded even more, it will cover more wavelengths than the yellow semichrome does, approaching white, until it is reached when the full spectrum is emitted or reflected. The described process is called "cumulation". Cumulation can be started at either end of the visible spectrum (we just described cumulation starting from the red end of the spectrum, generating the "warm" sharp edge), cumulation starting at the violet end of the spectrum will generate the "cold" sharp edge.[6]
Optimal color solid or Rösch–MacAdam color solid plotted within CIE 1931 XYZ color space, with D65white point. Notice the central symmetry of the solid, and the two sharp edges, one with warm colors and the other one with cold colors.
Maximum chroma colors, semichromes, or full colors
Each hue has a maximum chroma color, also known as maximum chroma point, semichrome, or full color; there are no colors of that hue with a higher chroma. They are the most chromatic, vibrant colors that we are able to see. Although we are, for now, unable to produce them, these are the colors that would be located in an ideal color wheel. They were called semichromes or full colors by the German chemist and philosopher Wilhelm Ostwald in the early 20th century.[6][7]
If B is the complementary wavelength of wavelength A, then the straight line that connects A and B passes through the achromatic axis in a linear color space, such as LMS or CIE 1931 XYZ. If the reflectance spectrum of a color is 1 (100%) for all the wavelengths between A and B, and 0 for all the wavelengths of the other half of the color space, then that color is a maximum chroma color, semichrome, or full color (this is the explanation to why they were called semichromes). Thus, maximum chroma colors are a type of optimal color.[6][7]
As explained, full colors are far from being monochromatic. If the spectral purity of a maximum chroma color is increased, its chroma decreases, because it will approach the visible spectrum, ergo, it will approach black.[6]
In perceptually uniform color spaces, the lightness of the full colors varies from around 30% in the violetish blue hues, to around 90% in the yellowish hues. The chroma of each maximum chroma point also varies depending on the hue; in optimal color solids plotted in perceptually uniform color spaces, semichromes like red, green, blue, violet, and magenta have a high chroma, while semichromes like yellow, orange, and cyan have a slightly lower chroma.
Slice of the Munsell color space in the hues of 5PB and 5Y. The point farthest from the achromatic axis in each of these two hue slices is the maximum chroma color, semichrome, or full color of that hue.
In color spheres and the HSL color space, the maximum chroma colors are located around the equator at the periphery of the color sphere. This makes color solids with a spherical shape inherently non-perceptually uniform, since they imply that all full colors have a lightness of 50%, when, as humans perceive them, there are full colors with a lightness from around 30% to around 90%. A perceptually uniform color solid has an irregular shape.[8][9]
History of the idea of the optimal color solid
In the beginning of the 20th century, industrial demands for a controllable way to describe colors and the new possibility to measure light spectra initiated intense research on mathematical descriptions of colors.
The idea of optimal colors was introduced by the Baltic German chemist Wilhelm Ostwald. Erwin Schrödinger showed in his 1919 article Theorie der Pigmente von größter Leuchtkraft (Theory of Pigments with Highest Luminosity)[5] that the most-saturated colors that can be created with a given total reflectivity are generated by surfaces having either zero or full reflectance at any given wavelength, and the reflectivity spectrum must have at most two transitions between zero and full.
Schrödinger's work was further developed by David MacAdam and Siegfried Rösch[Wikidata].[10] MacAdam was the first person to calculate precise coordinates of selected points on the boundary of the optimal color solid in the CIE 1931 color space for lightness levels from Y = 10 to 95 in steps of 10 units. This enabled him to draw the optimal color solid at an acceptable degree of precision. Because of his achievement, the boundary of the optimal color solid is called the MacAdam limit (1935).
On modern computers, it is possible to calculate an optimal color solid with great precision in seconds. Usually, only the MacAdam limit (the optimal colors, the boundary of the Optimal color solid) are computed, because all the other (non-optimal) colors exist inside the boundary.
The color solid can also be used to clearly visualize the volume or gamut of a screen, printer, the human eye, etc, because it gives information about the dimension of lightness, whilst the commonly used chromaticity diagram lacks this dimension of color.
Artists and art critics find the color solid to be a useful means of organizing the three variables of color—hue, lightness (or value), and saturation (or chroma), as modelled in the HCL and HSL color models—in a single schematic, using it as an aid in the composition and analysis of visual art.
See also
Wikimedia Commons has media related to Color solids .
Color or colour is the visual perception based on the electromagnetic spectrum. Though color is not an inherent property of matter, color perception is related to an object's light absorption, reflection, emission spectra, and interference. For most humans, colors are perceived in the visible light spectrum with three types of cone cells (trichromacy). Other animals may have a different number of cone cell types or have eyes sensitive to different wavelengths, such as bees that can distinguish ultraviolet, and thus have a different color sensitivity range. Animal perception of color originates from different light wavelength or spectral sensitivity in cone cell types, which is then processed by the brain.
A set of primary colors or primary colours consists of colorants or colored lights that can be mixed in varying amounts to produce a gamut of colors. This is the essential method used to create the perception of a broad range of colors in, e.g., electronic displays, color printing, and paintings. Perceptions associated with a given combination of primary colors can be predicted by an appropriate mixing model that reflects the physics of how light interacts with physical media, and ultimately the retina. The most common color mixing models are the additive primary colors and the subtractive primary colors. Red, yellow and blue are also commonly taught as primary colours, despite some criticism due to its lack of scientific basis.
A pigment is a powder used to add color or change visual appearance. Pigments are completely or nearly insoluble and chemically unreactive in water or another medium; in contrast, dyes are colored substances which are soluble or go into solution at some stage in their use. Dyes are often organic compounds whereas pigments are often inorganic. Pigments of prehistoric and historic value include ochre, charcoal, and lapis lazuli.
In color theory, hue is one of the main properties of a color, defined technically in the CIECAM02 model as "the degree to which a stimulus can be described as similar to or different from stimuli that are described as red, orange, yellow, green, blue, violet," within certain theories of color vision.
In colorimetry, the Munsell color system is a color space that specifies colors based on three properties of color: hue, value (lightness), and chroma. It was created by Albert H. Munsell in the first decade of the 20th century and adopted by the United States Department of Agriculture (USDA) as the official color system for soil research in the 1930s.
HSL and HSV are the two most common cylindrical-coordinate representations of points in an RGB color model. The two representations rearrange the geometry of RGB in an attempt to be more intuitive and perceptually relevant than the cartesian (cube) representation. Developed in the 1970s for computer graphics applications, HSL and HSV are used today in color pickers, in image editing software, and less commonly in image analysis and computer vision.
Color vision, a feature of visual perception, is an ability to perceive differences between light composed of different frequencies independently of light intensity.
The CIELAB color space, also referred to as L*a*b*, is a color space defined by the International Commission on Illumination in 1976. It expresses color as three values: L* for perceptual lightness and a* and b* for the four unique colors of human vision: red, green, blue and yellow. CIELAB was intended as a perceptually uniform space, where a given numerical change corresponds to a similar perceived change in color. While the LAB space is not truly perceptually uniform, it nevertheless is useful in industry for detecting small differences in color.
In color reproduction and colorimetry, a gamut, or color gamut, is a convex set containing the colors that can be accurately represented, i.e. reproduced by an output device or measured by an input device. Devices with a larger gamut can represent more colors. Similarly, gamut may also refer to the colors within a defined color space, which is not linked to a specific device. A trichromatic gamut is often visualized as a color triangle. A less common usage defines gamut as the subset of colors contained within an image, scene or video.
In color science, the dominant wavelength is a method of approximating a color's hue. Along with purity, it makes up one half of the Helmholtz coordinates. A color's dominant wavelength is the wavelength of monochromatic spectral light that, if plotted in a chromaticity diagram, the straight line that passes through the color in question and the white point will also pass through this wavelength.
Colorfulness, chroma and saturation are attributes of perceived color relating to chromatic intensity. As defined formally by the International Commission on Illumination (CIE) they respectively describe three different aspects of chromatic intensity, but the terms are often used loosely and interchangeably in contexts where these aspects are not clearly distinguished. The precise meanings of the terms vary by what other functions they are dependent on.
A spectral color is a color that is evoked by monochromatic light, i.e. either a spectral line with a single wavelength or frequency of light in the visible spectrum, or a relatively narrow spectral band. Every wave of visible light is perceived as a spectral color; when viewed as a continuous spectrum, these colors are seen as the familiar rainbow. Non-spectral colors are evoked by a combination of spectral colors.
In color science, a color model is an abstract mathematical model describing the way colors can be represented as tuples of numbers, typically as three or four values or color components. When this model is associated with a precise description of how the components are to be interpreted, taking account of visual perception, the resulting set of colors is called "color space."
In 1931 the International Commission on Illumination (CIE) published the CIE 1931 color spaces which define the relationship between the visible spectrum and the visual sensation of specific colors by human color vision. The CIE color spaces are mathematical models that create a "standard observer", which attempts to predict the perception of unique hues of color. These color spaces are essential tools that provide the foundation for measuring color for industry, including inks, dyes, and paints, illumination, color imaging, etc. The CIE color spaces contributed to the development of color television, the creation of instruments for maintaining consistent color in manufacturing processes, and other methods of color management.
The Coloroid Color System is a color space developed between 1962 and 1980 by Antal Nemcsics at the Budapest University of Technology and Economics for use by "architects and visual constructors". Since August 2000, the Coloroid has been registered as Hungarian Standard MSZ 7300.
A color space is a specific organization of colors. In combination with color profiling supported by various physical devices, it supports reproducible representations of color – whether such representation entails an analog or a digital representation. A color space may be arbitrary, i.e. with physically realized colors assigned to a set of physical color swatches with corresponding assigned color names, or structured with mathematical rigor. A "color space" is a useful conceptual tool for understanding the color capabilities of a particular device or digital file. When trying to reproduce color on another device, color spaces can show whether shadow/highlight detail and color saturation can be retained, and by how much either will be compromised.
In color theory, the line of purples or purple boundary is the locus on the edge of the chromaticity diagram formed between extreme spectral red and violet. Except for these endpoints of the line, colors on the line are non-spectral. Rather, every color on the line is a unique mixture in a ratio of fully saturated red and fully saturated violet, the two spectral color endpoints of visibility on the spectrum of pure hues. Colors on the line and spectral colors are the only ones that are fully saturated in the sense that, for any point on the line, no other possible color being a mixture of red and violet is more saturated than it.
Impossible colors are colors that do not appear in ordinary visual functioning. Different color theories suggest different hypothetical colors that humans are incapable of perceiving for one reason or another, and fictional colors are routinely created in popular culture. While some such colors have no basis in reality, phenomena such as cone cell fatigue enable colors to be perceived in certain circumstances that would not be otherwise.
A color appearance model (CAM) is a mathematical model that seeks to describe the perceptual aspects of human color vision, i.e. viewing conditions under which the appearance of a color does not tally with the corresponding physical measurement of the stimulus source.
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