CIEHLC Cylindrical Colour Spaces

The CIELCh or CIEHLC is a colour space based on either CIELUV or CIELAB, which uses polar coordinates \(C^*\) (chroma/relative saturation) and \(h\degree\) (hue angle/angle of hue in the CIELUV/CIELAB colour wheel) instead of the cartesian coordinates \(u^*\) and \(v^*\)/\(a^*\) and \(b^*\). The brightness \(L^*\) remains unchanged.

\(\text{CIELCh}_{ab}\) - Cylindrical CIELAB
\(\text{CIELCh}_{uv}\) - Cylindrical CIELUV

Conversion

For CIELUV HLC
\(C^*_{uv}=\sqrt{{u^*}^2+{v^*}^2}\)
\(h\degree_{uv}=atan(v^*/u^*)\)

Furthermore, saturation correlate can be written as:
\(s_{uv}=\frac{C^*_{uv}}{L^*} = 13\sqrt{(u'-u'_n)+(v'-v'_n)^2}\)
No such correlation for saturation exists for CIELAB HLC

For CIELAB HLC:
\(C^*_{ab}=\sqrt{{a^*}^2+{b^*}^2}\)
\(h\degree_{ab}=atan(b^*/a^*)\)

\(a^*=C^*cos(h\degree)\)
\(b^*=C^*sin(h\degree)\)