A color solid is the

three-dimensional In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (''coordinates'') are required to determine the position (geometry), position of a point (geometry), poi ...

representation of a

color space A color space is a specific organization of colors. In combination with color profiling supported by various physical devices, it supports reproducible representations of colorwhether such representation entails an analog or a digital represe ...

model A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin , . Models can be divided in ...

and can be thought as an analog of, for example, the

one-dimensional A one-dimensional space (1D space) is a mathematical space in which location can be specified with a single coordinate. An example is the number line, each point of which is described by a single real number. Any straight line or smooth curv ...

color wheel A color wheel or color circle is an abstract illustrative organization of color hues around a circle, which shows the relationships between primary colors, secondary colors, tertiary colors etc. Some sources use the terms ''color wheel'' an ...

, which depicts the variable of

hue In color theory, hue is one of the properties (called color appearance parameters) of a color, defined 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 ...

(similarity with red, yellow, green, blue, etc.); or the 2D

chromaticity diagram Chromaticity is an objective specification of the quality of a color regardless of its luminance. Chromaticity consists of two independent parameters, often specified as ''hue'' (''h'') and ''colorfulness'' (''s''), where the latter is alter ...

(or the

color triangle A color triangle is an arrangement of colors within a triangle, based on the additive or subtractive combination of three primary colors at its corners. An additive color space defined by three primary colors has a chromaticity gamut that is ...

), which depicts the variables of hue and

spectral purity Spectral purity is a term used in both optics and signal processing. In optics, it refers to the quantification of the monochromaticity of a given light sample. This is a particularly important parameter in areas like laser operation and time mea ...

. The added

spatial dimension In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...

allows a color solid to depict the three dimensions of color: lightness (gradations of light and dark, tints or shades), hue, and

colorfulness 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 ...

, allowing the solid to depict all conceivable colors in an organized three-dimensional structure.

Organization

Different color theorists have each designed unique color solids. Many are in the shape of a

sphere A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

, 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

Philipp Otto Runge Philipp Otto Runge (; 1777–1810) was a German artist, draftsman, painter, and color theorist. Runge and Caspar David Friedrich are often regarded as the leading painters of the German Romantic movement.Koerner, Joseph Leo. 1990. ''Caspar Davi ...

and

Johannes Itten Johannes Itten (11 November 1888 – 25 March 1967) was a Swiss expressionist painter, designer, teacher, writer and theorist associated with the Bauhaus (''Staatliches Bauhaus'') school. Together with German-American painter Lyonel Feining ...

are typical examples and prototypes for many other color solid schematics. 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 An axis (: axes) may refer to: Mathematics *A specific line (often a directed line) that plays an important role in some contexts. In particular: ** Coordinate axis of a coordinate system *** ''x''-axis, ''y''-axis, ''z''-axis, common names ...

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 In digital photography, computer-generated imagery, and colorimetry, a greyscale (more common in Commonwealth English) or grayscale (more common in American English) image is one in which the value of each pixel is a single sample (signal), s ...

. 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. File:Sphere vertical cross section runge.svg,

's ''Farbenkugel'' File:Sphere vertical cross section munsell.svg,

Albert Henry Munsell Albert Henry Munsell (January 6, 1858 – June 28, 1918) was an American painter, teacher of art, and the inventor of the Munsell color system. He was born in Boston, Massachusetts, attended and served on the faculty of Massachusetts Normal Art ...

's ''color sphere'' File:Sphere vertical cross section itten.svg,

's ''color sphere'' File:Sphere vertical cross section parametric.svg,

Spherical coordinate system In mathematics, a spherical coordinate system specifies a given point in three-dimensional space by using a distance and two angles as its three coordinates. These are * the radial distance along the line connecting the point to a fixed point ...

(for comparison)

Optimal color solid

The optimal color solid or Rösch–

MacAdam Macadam is a type of road construction pioneered by Scottish engineer John Loudon McAdam , in which crushed stone is placed in shallow, convex layers and compacted thoroughly. A binding layer of stone dust (crushed stone from the original mat ...

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. For now, we are unable to produce objects with such colors, at least not without recurring to more complex physical phenomena. ''*(with classical reflection. Phenomena like

fluorescence Fluorescence is one of two kinds of photoluminescence, the emission of light by a substance that has absorbed light or other electromagnetic radiation. When exposed to ultraviolet radiation, many substances will glow (fluoresce) with colore ...

structural coloration Structural coloration in animals, and a few plants, is the production of colour by microscopically structured surfaces fine enough to interfere with visible light instead of Biological pigment, pigments, although some structural coloration occu ...

may cause the color of objects to lie outside the optimal color solid)'' The

reflectance spectrum The reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at the boundary. Reflectance is a component of the response of the electronic ...

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. 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 color 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 (e.g. lasers). Every wave of visible ...

s and follow roughly the horseshoe-shaped portion of the CIE xy chromaticity diagram (the

spectral locus 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 (e.g. lasers). Every wave of visible ...

), but are, in surfaces, more

chromatic Diatonic and chromatic are terms in music theory that are used to characterize scales. The terms are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, es ...

, 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 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 (no mono ...

), leading to

magenta Magenta () is a purple-red color. On color wheels of the RGB color model, RGB (additive) and subtractive color, CMY (subtractive) color models, it is located precisely midway between blue and red. It is one of the four colors of ink used in colo ...

or purple-like colors. Rechteckspektrum_sRGB

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 chromaticity diagram). In linear color spaces, such as LMS or CIE 1931 XYZ, the set of

rays Ray or RAY may refer to: Fish * Ray (fish), any cartilaginous fish of the superorder Batoidea * Ray (fish fin anatomy), the bony or horny spine on ray-finned fish Science and mathematics * Half-line (geometry) or ray, half of a line split at an ...

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 Symmetry () in everyday life refers to a sense of harmonious and beautiful proportion and balance. In mathematics, the term has a more precise definition and is usually used to refer to an object that is invariant under some transformations ...

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. 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 Warm, WARM, or Warmth may refer to: * A somewhat high temperature; heat * Kindness Music Albums * ''Warm'' (Herb Alpert album), 1969 * ''Warm'' (Jeff Tweedy album), 2018 * ''Warm'' (Johnny Mathis album), 1958, and the title song * ''Warm'' (T ...

" edge, which goes from black, to red, to orange, to yellow, to white; and the "

cold Cold is the presence of low temperature, especially in the atmosphere. In common usage, cold is often a subjectivity, subjective perception. A lower bound to temperature is absolute zero, defined as 0.00K on the Kelvin scale, an absolute t ...

" edge, which goes from black, to deep

violet Violet may refer to: Common meanings * Violet (color), a spectral color with wavelengths shorter than blue * One of a list of plants known as violet, particularly: ** ''Viola'' (plant), a genus of flowering plants Places United States * Vi ...

, to blue, to

cyan Cyan () is the color between blue and green on the visible spectrum of light. It is evoked by light with a predominant wavelength between 500 and 520 nm, between the wavelengths of green and blue. In the subtractive color system, or CMYK c ...

, 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 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.

Maximum chroma colors, semichromes, or full colors

Each hue has a maximum chroma point, semichrome, or full color; objects cannot have a color of that hue with a higher chroma. They are the most chromatic, vibrant colors that objects can have. They were called semichromes or full colors by the German chemist and philosopher

Wilhelm Ostwald Wilhelm Friedrich Ostwald (; – 4 April 1932) was a Latvian chemist and philosopher. Ostwald is credited with being one of the founders of the field of physical chemistry, with Jacobus Henricus van 't Hoff, Walther Nernst and Svante Arrhenius. ...

in the early 20th century. 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 One half is the multiplicative inverse of 2. It is an irreducible fraction with a numerator of 1 and a denominator of 2. It often appears in mathematical equations, recipes and measurements. As a word One half is one of the few fractions w ...

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. 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. 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

yellow Yellow is the color between green and orange on the spectrum of light. It is evoked by light with a dominant wavelength of roughly 575585 nm. It is a primary color in subtractive color systems, used in painting or color printing. In t ...

ish 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

have a high chroma, while semichromes like yellow, orange, and

have a slightly lower chroma. Munsell 5 PB 5Y

In color spheres and the

HSL color space 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 ...

, 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 In color science, color difference or color distance is the separation between two colors. This metric allows quantified examination of a notion that formerly could only be described with adjectives. Quantification of these properties is of great ...

, since they imply that all full colors have a

lightness Lightness is a visual perception of the luminance (L) of an object. It is often judged relative to a similarly lit object. In colorimetry and color appearance models, lightness is a prediction of how an illuminated color will appear to a stand ...

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.

History of the idea of optimal colors

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

Erwin Schrödinger Erwin Rudolf Josef Alexander Schrödinger ( ; ; 12 August 1887 – 4 January 1961), sometimes written as or , was an Austrian-Irish theoretical physicist who developed fundamental results in quantum field theory, quantum theory. In particul ...

showed in his 1919 article ' (Theory of Pigments with Highest Luminosity) 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 David Lewis MacAdam (July 1, 1910 – March 9, 1998) was an American physicist and color scientist who made important contributions to color science and technology in the fields of colorimetry, color discrimination, color photography and televis ...

and . 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 limits (the optimal colors, the boundary of the optimal color solid) are computed, because all the other (non-optimal) possible surface colors exist inside the boundary.

Color volume

Color volume is the set of all available color at all available

saturation Saturation, saturated, unsaturation or unsaturated may refer to: Chemistry *Saturated and unsaturated compounds, a classification of compounds related to their ability to resist addition reactions ** Degree of unsaturation **Saturated fat or satu ...

, and

brightness Brightness is an attribute of visual perception in which a source appears to be radiating/reflecting light. In other words, brightness is the perception dictated by the luminance of a visual target. The perception is not linear to luminance, and ...

, especially when referring to a specific gamut. It's the result of a 2D

or 2D

color gamut 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 (e.g. printer or display) or measured by an input device (e.g. ...

(that represent

chromaticity Chromaticity is an objective specification of the quality of a color regardless of its luminance. Chromaticity consists of two independent parameters, often specified as '' hue'' (''h'') and ''colorfulness'' (''s''), where the latter is alte ...

) combined with the

dynamic range Dynamics (from Greek δυναμικός ''dynamikos'' "powerful", from δύναμις ''dynamis'' " power") or dynamic may refer to: Physics and engineering * Dynamics (mechanics), the study of forces and their effect on motion Brands and ent ...

. The term has been used to describe HDR's higher color volume than SDR (i.e. peak brightness of at least 1,000 cd/m² higher than SDR's 100 cd/m² limit and wider color gamut than

Rec. 709 ITU-R Recommendation 709, usually abbreviated Rec. 709, BT.709, or ITU-R 709, is a standard developed by the Radiocommunication Sector of the International Telecommunication Union (ITU-R) for image encoding and signal characteristics ...

sRGB sRGB (standard RGB) is a colorspace, for use on monitors, printers, and the World Wide Web. It was initially proposed by HP and Microsoft in 1996 and became an official standard of the International Electrotechnical Commission (IEC) as IEC 6 ...

Usage

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 HCL may refer to: Science and medicine * Hairy cell leukemia, an uncommon and slowly progressing B cell leukemia * Harvard Cyclotron Laboratory, from 1961 to 2002, a proton accelerator used for research and development * Hollow-cathode lamp, a s ...

and HSL color models—in a single schematic, using it as an aid in the composition and analysis of visual art.

Gallery

File:Atlas of the Munsell Color System page 13.jpg, 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.Kuehni (2002), p. 21 File:Runge Farbenkugel.jpg,

’s ''Farbenkugel'' (color sphere), 1810, showing the surface of the sphere (top two images), and horizontal and vertical cross sections (bottom two images) File:Tape Ball Color Space, Itten, 1919-20.jpg, Color sphere of

, 1919–20. A much clearer representation of his model appears in ''The Art of Color'', 1961, which cannot be reproduced here for copyright reasons. File:Color Sphere.jpg, Color sphere modeled in salt dough by Jesse Hensel, 2011 File:Color Sphere Section.jpg, Section of Hensel's sphere revealing some of the desaturated colors

References

External links

Runge's Color Sphere
(Java applet does not work in all Web browsers) {{Color topics

solid Solid is a state of matter where molecules are closely packed and can not slide past each other. Solids resist compression, expansion, or external forces that would alter its shape, with the degree to which they are resisted dependent upon the ...

Color space