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# Hue

[hyoo or, often, yoo]
Hue, city (1989 pop. 260,489), former capital of the historic region of Annam, Vietnam, in a rich farming area on the Hue River near the South China Sea. Probably founded in the 3d cent. A.D., Hue was occupied in turn by the Chams and the Annamese. After the 16th cent. it was the seat of a dynasty that extended its power over S Annam, modern Cochin China, and parts of Cambodia and Laos. The first king of Vietnam, Nguyen Anh, was crowned there in 1802, and shortly thereafter Hue became the capital of the new kingdom, emerging as an artistic and literary center. The French occupied the city in 1883. During World War II the Japanese mined iron ore in the area. In the Vietnam War, Hue was the scene of the longest and heaviest fighting of the Tet offensive (Jan.-Feb., 1968); some 4,000 civilians were killed and most of the city, including the palaces and tombs of the former Annamese kings, was destroyed. Much of the city has been rebuilt. Hue has an important airport and is the seat of the Univ. of Hue.

Hue is one of the main properties of a color described with names such as "red", "yellow", etc. The two other main properties are lightness and colorfulness. Hue is also one of the three dimensions in some colorspaces along with saturation, and lightness.

Usually, colors with the same hue are distinguished with adjectives referring to their lightness and/or chroma, such as with "light blue", "pastel blue", "vivid blue". Exceptions include brown, which is a dark orange, and pink, a light red with reduced chroma.

In painting color theory, a hue refers to a pure color—one without tint or shade (added white or black pigment, respectively). A hue is an element of the color wheel.

## Computing hue

In opponent color spaces in which two of the axes are perceptually orthogonal to lightness, such as CIE L*a*b* (CIELAB) and CIE L*u*v* (CIELUV), 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:

$tan h_\left\{ab\right\} = frac\left\{b^*\right\}\left\{a^*\right\}$

while, analogously, in CIELUV:

$tan h_\left\{uv\right\} = frac\left\{v^*\right\}\left\{u^*\right\} = frac\left\{v\text{'}\right\}\left\{u\text{'}\right\}$

In practice, a four-quadrant arctangent may be used if available to invert these formulae.

### Computing hue from 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°, one may solve:

$tan h_\left\{Preucil hexagon\right\} = frac\left\{sqrt\left\{3\right\}cdot \left(G - B\right)\right\}\left\{2cdot R - G - B\right\}$

He also used a polar plot, which he termed a color circle. Using R, G, and B, rather than the R, G, and B densities Preucil used, 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 appropriate formula; see table below.

Ordering Hue Region Formula
$R ge G ge B$ Red-Yellow $h_\left\{Preucil circle\right\} = 60^\left\{circ\right\} cdot frac\left\{G - B\right\}\left\{R - B\right\}$
$G > R ge B$ Yellow-Green $h_\left\{Preucil circle\right\} = 60^\left\{circ\right\} cdot left\left(1 + frac\left\{R - B\right\}\left\{G - B\right\}right\right)$
$G ge B > R$ Green-Cyan $h_\left\{Preucil circle\right\} = 60^\left\{circ\right\} cdot left\left(2 + frac\left\{B - R\right\}\left\{G - R\right\}right\right)$
$B > G > R$ Cyan-Blue $h_\left\{Preucil circle\right\} = 60^\left\{circ\right\} cdot left\left(3 + frac\left\{G - R\right\}\left\{B - R\right\}right\right)$
$B > R ge G$ Blue-Magenta $h_\left\{Preucil circle\right\} = 60^\left\{circ\right\} cdot left\left(4 + frac\left\{R - G\right\}\left\{B - G\right\}right\right)$
$R ge B > G$ Magenta-Red $h_\left\{Preucil circle\right\} = 60^\left\{circ\right\} cdot left\left(5 + frac\left\{B - G\right\}\left\{R - G\right\}right\right)$

Note that in each case the formula contains the fraction $frac\left\{M - L\right\}\left\{H - L\right\}$, 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 degrees (red, yellow, green, cyan, blue, magenta, and the colors mid-way between contiguous pairs), and differ by approximately 1.2 degrees at odd integer multiples of 15 degrees (based on the circle formula), the maximum 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. The formulae used are those in the table above.

## Specialized hues

The hues exhibited by caramel colorings and beers are fairly limited in range. The Linner hue index is used to quantify the hue of such products.

## Hue as a qualification in the names of artist's colors

Manufacturers of pigments use the word hue e.g. 'Cadmium Yellow (hue)' to indicate that the original pigmentation ingredient, often toxic, has been replaced by safer (or cheaper) alternatives whilst retaining the hue of the original. Replacements are often used for chromium, cadmium and alizarin.

## Hue vs. dominant wavelength

Dominant wavelength (or sometimes equivalent wavelength) is a physical analog to the perceptual attribute hue. On a chromaticity diagram, a line is drawn from a white point through the coordinates of the color in question, until it intersects the spectral locus. The wavelength at which the line intersects the spectrum locus is identified as the color's dominant wavelength if the point is on the same side of the white point as the spectral locus, and as the color's complementary wavelength if the point is on the opposite side.

## Hue difference: $Delta h$ or $Delta H^*$?

There are two main ways in which hue difference is quantified. The first is the simple difference between the two hue angles. The symbol for this expression of hue difference is $Delta h_\left\{ab\right\}$ in CIELAB and $Delta h_\left\{uv\right\}$ in CIELUV. The other is computed as the residual total color difference after Lightness and Chroma differences have been accounted for; its symbol is $Delta H^*_\left\{ab\right\}$ in CIELAB and $Delta H^*_\left\{uv\right\}$ in CIELUV.