Editing Chromaticity (section)

==Quantitative description==
In color science, the [[white point]] of an illuminant or of a display is a neutral reference characterized by a chromaticity; all other chromaticities may be defined in relation to this reference using [[Polar coordinate system|polar coordinates]]. The ''hue'' is the angular component, and the ''purity'' is the radial component, normalized{{clarify|date=June 2013|reason=note that the chromaticity space does not have a canonical affine structure, so there are no invariantly defined ratios of lengths even along the same line}} by the maximum radius for that hue.

''Purity'' is roughly equivalent to the term ''[[Colorfulness#Saturation|saturation]]'' in the [[HSL and HSV|HSV color model]]. The property ''[[hue]]'' is as used in general color theory and in specific [[color model]]s such as [[HSL and HSV]] color spaces, though it is more [[Color difference#Tolerance|perceptually uniform]] in color models such as [[Munsell color system|Munsell]], [[CIELAB color space|CIELAB]] or [[CIECAM02]].

Some [[color space]]s separate the three dimensions of color into one [[relative luminance|luminance]] dimension and a pair of chromaticity dimensions. For example, the white point of an [[sRGB]] display is an {{mvar|x}}, {{mvar|y}} chromaticity of (0.3127, 0.3290), where {{mvar|x}} and {{mvar|y}} coordinates are used in the xyY space.

[[Image:CIE 1976 UCS.png|right|thumb|240px|{{math|(''u′'', ''v′'')}}, the chromaticity in [[CIELUV]], is a fairly [[Color difference#Tolerance|perceptually uniform]] presentation of the chromaticity as (another than in CIE 1931) planar [[Euclidean space|Euclidean]] shape. This presentation is a [[projective transformation]] of the CIE 1931 chromaticity diagram above.]]

These pairs determine a chromaticity as [[affine coordinates]] on a [[triangle]] in a [[Plane (mathematics)|2D-space]], which contains all possible chromaticities. These {{mvar|x}} and {{mvar|y}} are used because of simplicity of expression in [[CIE 1931 color space|CIE 1931]] (see below) and have no inherent advantage. Other [[coordinate system]]s on the same X-Y-Z triangle, or other [[color triangle]]s, can be used.

On the other hand, some color spaces such as [[RGB color spaces|RGB]] and [[CIE 1931 color space#Definition of the CIE XYZ color space|XYZ]] do not separate out chromaticity, but chromaticity is defined by a [[projectivization|mapping that normalizes out intensity]], and its coordinates, such as {{mvar|r}} and {{mvar|g}} or {{mvar|x}} and {{mvar|y}}, can be calculated through the [[division (mathematics)|division]] operation, such as {{math|1=''x'' =}}&nbsp;{{sfrac|''X''|''X'' + ''Y'' + ''Z''}}, and so on.

The xyY space is a cross between the CIE XYZ and its normalized chromaticity coordinates xyz, such that the luminance Y is preserved and augmented with just the required two chromaticity dimensions.<ref>{{cite book | title = Digital Video and HDTV: Algorithms and Interfaces | author = Charles A. Poynton | publisher = Morgan Kaufmann | year = 2003 | isbn = 978-1-55860-792-7 | url = https://books.google.com/books?id=ra1lcAwgvq4C&q=chromaticity+xyy&pg=RA1-PA219 }}</ref>