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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 ...
or
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
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 (similarity with red, yellow, green, blue, etc.); or the 2D chromaticity diagram (or the color triangle), which depicts the variables of hue and spectral purity. 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 and Johannes Itten 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, Philipp Otto Runge's ''Farbenkugel'' File:Sphere vertical cross section munsell.svg, Albert Henry Munsell's ''color sphere'' File:Sphere vertical cross section itten.svg, Johannes Itten'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 ...
or
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 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), 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), 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. 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 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" 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, 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 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
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 ...
have a high chroma, while semichromes like yellow, orange, and
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 ...
have a slightly lower chroma. 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 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
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. ...
.
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 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 hue, saturation,
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 ...
, 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
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 ...
or 2D color gamut (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 /
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 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, 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) File:Tape Ball Color Space, Itten, 1919-20.jpg, 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. 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


See also

*
Color model 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 ...
* Color triangle *
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 ...


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