Hue

Hue can typically be represented quantitatively by a single number, often corresponding to an angular position around a central or neutral point or axis on a color space coordinate diagram (such as a chromaticity diagram) or color wheel, or by its dominant wavelength or by that of its complementary color. The other color appearance parameters are colorfulness, saturation (also known as intensity or chroma), lightness, and brightness. Usually, colors with the same hue are distinguished with adjectives referring to their lightness or colorfulness – for example: "light blue", "pastel blue", "vivid blue", and "cobalt blue". Exceptions include brown, which is a dark orange.

In painting, a hue is a pure pigment—one without tint or shade, which add white or black pigment, respectively.

The human brain first processes hues in areas in the extended V4 called globs.

Deriving a hue

The concept of a color system with a hue was explored as early as 1830 with Philipp Otto Runge's color sphere. The Munsell color system from the 1930s was a great step forward, as it was realized that perceptual uniformity means the color space can no longer be a sphere.

As a convention, the hue for red is set to 0° for most color spaces with a hue.

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

${\displaystyle h_{ab}=\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{n}2(b^{\ast },a^{\ast }),}$

while, analogously, in CIELUV

${\displaystyle h_{uv}=\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{n}2(v^{\ast },u^{\ast })=\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{n}2(v^{\prime },u^{\prime }),}$

where, atan2 is a two-argument inverse tangent.

Defining hue in terms of RGB

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

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

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. 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.

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.

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 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. The formulae used are those in the table above.

One might notice that the HSL/HSV hue "circle" does not appear to all be of the same lightness. This is a known issue of this RGB-based derivation of hue.