# Hue

For the city in Vietnam, see Hue (city).

A hue refers to the gradation of color within the optical spectrum, or visible spectrum, of light. "Hue" may also refer to a particular color within this spectrum, as defined by its dominant wavelength, or the central tendency of its combined wavelengths. For example, a light wave with a central tendency within 565-590 nm will be yellow.

In painting color theory, a hue refers to a pure color —one without added white (tint) or black (shade) pigment.

In an RGB color space, hue can be thought of as an angle φ in standard position. To calculate φ, let R, G, B be the color coordinates in RGB space, defined on a scale from zero to one. Then, after obtaining the brightness μ and the saturation σ, the hue could be obtained from

[itex] \phi = \arccos \left( {R - \mu \over \sigma \sqrt{2}} \right) [itex]

(Compare with standard score). Using this formula, φ=0 (in radians) would correspond to red, while φ=2π/3 would correspond to blue, and φ=4π/3 would correspond to green.

The RGB coordinates should be derivable from the μ, σ, φ coordinates as follows:

[itex] R = \mu + \sigma \sqrt{2} \cos \phi, [itex]
[itex] G = \mu + \sigma \sqrt{2} \cos \left( \phi + {4 \pi \over 3} \right), [itex]
[itex] B = \mu + \sigma \sqrt{2} \cos \left( \phi + {2 \pi \over 3} \right). [itex]

Hue is a coordinate (an angle of rotation) in HSB color space.

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