Dominant wavelength
In color science, the dominant wavelength is a method of approximating a color's hue. Along with purity, it makes up one half of the Helmholtz coordinates. The dominant wavelength of a given color is defined to be the wavelength of monochromatic spectral light that lies on the straight line passing through the white point and the given colour in the chromaticity diagram.
Determination
Helmholtz coordinates
The Helmholtz coordinates are a polar coordinate system for defining a 2D chromaticity plane. The circumferential coordinate is the dominant wavelength, which is analogous to hue of the HSV color space. The radial coordinate is the purity, which is analogous to saturation of the HSV color space.Color space
Not all color spaces can be used for determining the dominant wavelength of a color, because in most approximately perceptually uniform color spaces two colors with the same hue can have slightly different dominant wavelengths. Unless otherwise stated, the CIE 1931 color space is used., but the CIELUV color space is sometimes used. The LMS color space can also be used for this purpose.Calculation
To calculate the dominant wavelength of a chromaticity, a half straight line is drawn on the chromaticity diagram that passes through the chromaticity's coordinates and starts in the white point. The line is then extrapolated so it intersects the perimeter of the diagram at one point, where the perimeter comprises the spectral locus or the line of purples. The point of intersection of that line and the spectral locus is the dominant wavelength. If the line intersects with the line of purples and not the spectral locus, the complementary wavelength is used. The purity can then be calculated as defined here.White point
The white point is generally defined as—or assumed to be—equal energy white. This is defined as = in CIE xyY, and as = in XYZ color space. However, other white points may be used, generally defined by "white" standard illuminants or a color temperature such as 6500K.Complementary wavelength
When the chromaticity lies within the triangle with vertices at the white point, extreme spectral violet, and extreme spectral red, the dominant wavelength is indeterminate because the half straight line that passes through the white point and that chromaticity point intersects the limit of the visible gamut in the line of purples instead of the spectral locus. The colors on the line of purples cannot be defined by wavelength because they do not represent monochromatic light.Instead, the dominant wavelength is replaced with the complementary wavelength, which will represent the complementary color. To calculate it, the half straight line that starts on that chromaticity and passes through the white point is used; the intersection between this line and the spectral locus is the complementary wavelength. If a color doesn't have a dominant wavelength, its complementary color will.