section_path: Optimal colors
section_name: Optimal colors
paragraph_text: Optimal colors
  
  The gamut of the human color vision is bounded by optimal colors. They are the most chromatic colors that humans are able to see.
  
  The emission or reflectance spectrum of a color is the amount of light of each wavelength that it emits or reflects, in proportion to a given maximum, which has the value of 1 (100%). If the emission or 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: In the first, the transition goes from 0 at both ends of the spectrum to 1 in the middle, as shown in the image at right. In the second, it goes from 1 at the ends to 0 in the middle. In the third type, it starts at 1 at the red end of the spectrum, and it changes to 0 at a given wavelength. In the fourth type, it starts at 0 in the red end of the spectrum, and it changes to 1 at a given wavelength. 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 generally 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.
  
  The optimal color solid, Rösch – MacAdam color solid, or simply visible gamut, is a type of color solid that contains all the colors that humans are able to see. The optimal color solid is bounded by the set of all optimal colors.
  
  In optimal color solids, the colors of the visible spectrum are theoretically black, because their emission or reflection 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).
  
  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.
  
  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 deep violet, to blue, to cyan, to white. This is due to the following: If the portion of the emission or reflection 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 emission or 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 more, covering the green wavelengths, it will be seen as 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.