Editing CIELAB color space (section)

== Cylindrical model ==
<!-- redirect from [[LCHab]] -->
{{multiple image
| width = 150
| image1 = SRGB gamut within CIELCHab color space mesh.webm
| alt1 = SRGB gamut within CIELCHab color space
| thumbtime1 = 0
| image2 = Visible gamut within CIELCHab color space D65 whitepoint mesh.webm
| alt2 = Visible gamut within CIELCHab color space
| thumbtime2 = 0
| footer = The [[sRGB]] gamut (''left'') and [[Color solid#Optimal_color_solid|optimal color solid]] under D65 illumination (''right'') plotted within the CIELCHab color space. ''L'' is the vertical axis; ''C'' is the cylinder radius; ''h'' is the angle around the circumference.
}}

The "CIELCh" or "CIEHLC" space is a color space based on CIELAB, which uses the [[polar coordinates]] ''C''* ([[Colorfulness#Chroma|chroma]], colorfulness of the color) and ''h''° (hue angle, angle of the hue in the CIELAB color wheel) instead of the [[Cartesian coordinates]] ''a''* and ''b''*. The CIELAB lightness L* remains unchanged.

The conversion of ''a''* and ''b''* to ''C''* and ''h''° is performed as follows:

:<math>
  C^\star = \sqrt{{a^*}^2 + {b^*}^2}, \qquad
  h^\circ = \operatorname{atan}\left({b^*}/{a^*}\right)
</math>

Conversely, given the [[polar coordinates]], conversion to Cartesian coordinates is achieved with:

: <math>a^\star = C^\star \cos(h^\circ), \qquad b^\star = C^\star \sin(h^\circ)</math>

The LCh (or HLC) color space is not the same as the HSV, HSL or HSB color models, although their values can also be interpreted as a base color, saturation and lightness of a color. The HSL values are a polar coordinate transformation of what is technically defined RGB cube color space. LCh is still [[Color difference#Tolerance|perceptually uniform]].

{{multiple image
| width = 150
| image1 = CIEHLC polar.png
| alt1 = CIELCHab color space from top
| thumbtime1 = 0
| image2 = CIELHLC 3D.png
| alt2 = CIELCHab 3D color space
| thumbtime2 = 0
| footer = ''L'' is the vertical axis; ''C'' is the cylinder radius; ''h'' is the angle around the circumference.
}}
Further, ''H'' and ''h'' are not identical, because HSL space uses as primary colors the three additive primary colors red, green and blue (''H'' = 0, 120, 240°). Instead, the LCh system uses the four colors red, yellow, green and blue (''h'' = 0, 90, 180, 270°).  Regardless the angle ''h'', ''C'' = 0 means the achromatic colors (non saturated), that is, the gray axis.

The simplified spellings LCh, LCh(ab), LCH, LCH(ab) and HLC are common, but the letter presents a different order. [[HCL color space]] (Hue-Chroma-Luminance) on the other hand is a commonly used alternative name for the [[CIELUV#Cylindrical representation (CIELCh)|L*C*h(uv)]] color space, also known as the ''cylindrical representation'' or ''polar [[CIELUV]]''. This name is commonly used by [[information visualization]] practitioners who want to present data without the bias implicit in using varying [[Colorfulness|saturation]].<ref name="Zeileis2009">{{cite journal|last1=Zeileis|first1=Achim|last2=Hornik|first2=Kurt|last3=Murrell|first3=Paul|year=2009|title=Escaping RGBland: Selecting Colors for Statistical Graphics|url=http://epub.wu.ac.at/1692/1/document.pdf|journal=Computational Statistics & Data Analysis|volume=53|issue=9|pages=3259–3270|doi=10.1016/j.csda.2008.11.033}}</ref><ref>{{cite journal|last1=Stauffer|first1=Reto|last2=Mayr|first2=Georg J.|last3=Dabernig|first3=Markus|last4=Zeileis|first4=Achim|year=2015|title=Somewhere over the Rainbow: How to Make Effective Use of Colors in Meteorological Visualizations|url=https://www2.uibk.ac.at/downloads/c4041030/wpaper/2013-37.pdf|journal=Bulletin of the American Meteorological Society|volume=96|issue=2|pages=203–216|bibcode=2015BAMS...96..203S|doi=10.1175/BAMS-D-13-00155.1|hdl=10419/101098|hdl-access=free}}</ref> The name Lch(ab) is sometimes used to differentiate from L*C*h(uv).