Opponent color spaces

In opponent color spaces in which two of the axes are perceptually orthogonal to lightness, such as the CIE 1976 (L*, a*, b*) (CIELAB) and 1976 (L*, u*, v*) (CIELUV) color spaces, hue may be computed together with chroma by converting these coordinates from rectangular form to polar form. Hue is the angular component of the polar representation, while chroma is the radial component.

Specifically, in CIELAB^[7]

${\displaystyle h_{ab}=\mathrm {atan2} (b^{*},a^{*}),}$

while, analogously, in CIELUV^[7]

${\displaystyle h_{uv}=\mathrm {atan2} (v^{*},u^{*})=\mathrm {atan2} (v',u'),}$

where, atan2 is a two-argument inverse tangent.

Defining hue in terms of RGB

HSV color space as a conical object

An illustration of the relationship between the "hue" of colors with maximal saturation in HSV and HSL with their corresponding RGB coordinates

Hue circle in 24 colors (15°)

Preucil^[8] describes a color hexagon, similar to a trilinear plot described by Evans, Hanson, and Brewer,^[9] which may be used to compute hue from RGB. To place red at 0°, green at 120°, and blue at 240°,

${\displaystyle h_{rgb}=\mathrm {atan2} \left({\sqrt {3}}\cdot (G-B),2\cdot R-G-B\right).}$

Equivalently, one may solve

${\displaystyle \tan(h_{rgb})={\frac {{\sqrt {3}}\cdot (G-B)}{2\cdot R-G-B}}.}$

Preucil used a polar plot, which he termed a color circle.^[8] Using R, G, and B, one may compute hue angle using the following scheme: determine which of the six possible orderings of R, G, and B prevail, then apply the formula given in the table below.

Ordering	Hue region	${\displaystyle h_{\text{Preucil circle}}}$
${\displaystyle R\geq G\geq B}$	Orange	${\displaystyle 60^{\circ }\cdot {\frac {G-B}{R-B}}}$
${\displaystyle G>R\geq B}$	Chartreuse	${\displaystyle 60^{\circ }\cdot \left(2-{\frac {R-B}{G-B}}\right)}$
${\displaystyle G\geq B>R}$	Spring Green	${\displaystyle 60^{\circ }\cdot \left(2+{\frac {B-R}{G-R}}\right)}$
${\displaystyle \ B>G>R\ }$	Azure	${\displaystyle 60^{\circ }\cdot \left(4-{\frac {G-R}{B-R}}\right)}$
${\displaystyle B>R\geq G}$	Violet	${\displaystyle 60^{\circ }\cdot \left(4+{\frac {R-G}{B-G}}\right)}$
${\displaystyle R\geq B>G}$	Rose	${\displaystyle 60^{\circ }\cdot \left(6-{\frac {B-G}{R-G}}\right)}$

Note that in each case the formula contains the fraction ${\displaystyle {\frac {M-L}{H-L}}}$, where H is the highest of R, G, and B; L is the lowest, and M is the mid one between the other two. This is referred to as the "Preucil hue error" and was used in the computation of mask strength in photomechanical color reproduction.^[10]

Hue angles computed for the Preucil circle agree with the hue angle computed for the Preucil hexagon at integer multiples of 30° (red, yellow, green, cyan, blue, magenta, and the colors midway between contiguous pairs) and differ by approximately 1.2° at odd integer multiples of 15° (based on the circle formula), the maximal divergence between the two.

The process of converting an RGB color into an HSL color space or HSV color space is usually based on a 6-piece piecewise mapping, treating the HSV cone as a hexacone, or the HSL double cone as a double hexacone.^[11] The formulae used are those in the table above.

• Additional images for hue in the HSL and HSV systems
• 
  Hue in the HSL/HSV encodings of RGB
• 
  An image with the hues cyclically shifted in HSL space
• 
  The hues in this image of a painted bunting are cyclically rotated over time in HSL.

One might notice that the HSL/HSV hue "circle" do not appear to all be of the same brightness. This is a known issue of this RGB-based derivation of hue.^[12]