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 (such as
CIELAB,
Oklab,
CIECAM02, etc) two colors with the same hue can have slightly different dominant wavelengths. Unless otherwise stated, the
CIE 1931 color space (
CIEXYZ) is used., but the
CIELUV color space is sometimes used. 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 (illuminant E). This is defined as [x, y] = (1/3, 1/3) in
CIE xyY, and as [X, Y, Z] = (1, 1, 1) in
XYZ color space. However, other white points may be used, generally defined by "white"
standard illuminants or a
color temperature such as
6500K (D65).
Complementary wavelength When the chromaticity lies within the triangle with vertices at the white point, extreme spectral violet (360 nm), and extreme spectral red (780 nm), 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 (and it is not achromatic), its complementary color will. ==Application==