Editing Color (section)

== Optimal colors ==

{{main|Gamut#Surfaces (optimal colors)}}

Optimal colors are the most chromatic colors that surfaces can have. That is, optimal colors are the theoretical limit for the color of objects*.<ref name="new">{{cite journal |last1=Perales |first1=Esther |last2=Mora Estevan |first2=Teresa |last3=Viqueira Pérez |first3=Valentin |last4=de Fez |first4=Dolores |last5=Gilabert Pérez |first5=Eduardo José |last6=Martínez-Verdú |first6=Francisco M. |year=2005 |title=A new algorithm for calculating the MacAdam limits for any luminance factor, hue angle and illuminant |url=https://www.researchgate.net/publication/39435417 |journal=Repositorio Institucional de la Universidad de Alicante }}</ref> 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]] or [[structural coloration]] may cause the color of objects to lie outside the optimal color solid)''

The plot of the gamut bounded by optimal colors in a color space is called the optimal [[color solid]] or [[Siegfried Rösch|Rösch]]–[[David MacAdam|MacAdam]] color solid.

The [[Reflectance|reflectance spectrum]] of a color is the amount of light of each wavelength that it reflects, in proportion to a given maximum, which is total reflection of light of that wavelength, and 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.<ref name="sch">{{cite journal |last=Schrödinger |first=Erwin |year=1919 |title=Theorie der Pigmente größter Leuchtkraft |url=https://zenodo.org/record/1424357 |journal=Annalen der Physik |volume=367 |issue=15 |pages=603–622 |bibcode=1920AnP...367..603S |doi=10.1002/andp.19203671504}}</ref>

[[File:Rechteckspektrum_sRGB.svg|right|thumb|268x268px|Reflectance spectrum of a color-optimal reflective material. There is no known material with these properties, they are, for what we know, only theoretical.<ref name="thi">{{cite journal |last1=Koenderink |first1=Jan |last2=van Doorn |first2=Andrea J. |last3=Gegenfurtner |first3=Karl |year=2021 |title=RGB Colors and Ecological Optics |url=https://www.researchgate.net/publication/351231527 |journal=Frontiers in Computer Science |volume=3 |doi=10.3389/fcomp.2021.630370 |doi-access=free }}</ref>]]

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 [[Chromaticity diagram#The CIE xy chromaticity diagram|CIE xy chromaticity diagram]] (the [[spectral locus]]), but are, in surfaces, more [[colorfulness|chromatic]], although less [[Visible spectrum|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. The third type produces the colors located in the "warm" sharp edge of the optimal color solid (this will be explained later in the article). The fourth type produces the colors located in the "cold" sharp edge of the optimal color solid.

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).<ref name="thi"/>

In linear color spaces, such as [[LMS color space|LMS]] or [[CIE 1931 color space|CIE 1931 XYZ]], the set of [[Ray (geometry)|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 [[Symmetry|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.<ref name="thi"/>

[[File:Visible gamut within CIEXYZ color space D65 whitepoint mesh.webm|thumb|185x185px|Optimal color solid or Rösch–MacAdam color solid (with [[Illuminant D65|D65]] [[white point]]) plotted within [[CIE 1931 color space|CIE 1931 XYZ color space]]. Notice the central symmetry of the solid, and the two sharp edges, one with warm colors and the other one with cold colors.]]

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 "[[Heat|warm]]" edge, which goes from black, to red, to orange, to yellow, to white; and the "cold" edge, which goes from black, to deep [[Violet (color)|violet]], 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 reflectance is increased, now covering from the red end of the spectrum to the yellow wavelengths, it will be seen as red or orange. If the portion is expanded even more, covering some green wavelengths, it will be seen as yellow. If it is expanded even more, it will cover more wavelengths than the yellow [[Color solid#Maximum chroma colors, semichromes, or full colors|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.<ref name="thi"/>

[[File:Visible gamut within CIELUV color space D65 whitepoint mesh.webm|thumb|Optimal color solid plotted within the [[CIELUV color space|CIE L* u* v* color space]], with [[Illuminant D65|D65]] [[white point]]. Notice that it has two sharp edges, one with warm colors, and the other one with cold colors.|200x200px]]

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.

[[File:Optimal-color-solid,FL4,XYZ.gif|right|thumb|185x185px|MacAdam limits for illuminant [[Standard illuminant#Illuminant series F|CIE F4]] in [[CIE 1931 color space#CIE xyY color space|CIE xyY color space]]]]

=== 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]] in the early 20th century.<ref name="thi"/><ref name="Ost">{{cite journal |last1=Liberini |first1=Simone |last2=Rizzi |first2=Alessandro |year=2023 |title=Munsell and Ostwald colour spaces: A comparison in the field of hair colouring |url=https://onlinelibrary.wiley.com/doi/10.1002/col.22818|journal=Color Research and Application|volume=48 |pages=6–20 |doi=10.1002/col.22818 |hdl=2434/940227 |hdl-access=free }}</ref>

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 '''semi'''chromes). Thus, maximum chroma colors are a type of optimal color.<ref name="thi"/><ref name="Ost"/>

As explained, full colors are far from being monochromatic (physically, not perceptually). If the spectral purity of a semichrome is increased, its [[colorfulness|chroma]] decreases, because it will approach the visible spectrum, ergo, it will approach black.<ref name="thi"/>

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]]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, violet, and [[magenta]] have a high chroma, while semichromes like yellow, orange, and [[cyan]] have a slightly lower chroma.

[[File:Munsell 5 PB 5Y.png|thumb|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|200x200px]]