CIELCHab

CIELCHab is a cylindrical representation of the CIE Lab color space, mapping the Cartesian coordinates a and b to polar coordinates C (chroma) and h (hue). It preserves the perceptual meaning of lightness L while offering a more intuitive description of color tone for editing and visualization.

In this space, L remains in the typical range 0 to 100, where 0 is black and 100 is white. The chroma component C is defined as sqrt(a^2 + b^2) and is nonnegative. The hue angle h is computed as arctan2(b, a) and expressed in degrees, typically in the range 0 to 360. Hue indicates direction on the ab plane; 0° corresponds to red, 90° to yellow, 180° to green, and 270° to blue.

Conversions: Given L, C, h, the underlying a and b are a = C cos(h), b = C sin(h), with h in radians in the trigonometric functions; to store or transmit, convert degrees to radians when applying cos/sin. Conversely, C = sqrt(a^2 + b^2) and h = atan2(b, a) (converted to degrees).

Undefined hue occurs when C = 0 (a = b = 0); in that case hue is not defined and may be set to zero by convention.

Uses: CIELCHab is popular in color editing, palette design, and perceptual color difference calculations because changes in C and h correspond more closely to human perception of chroma and hue. It is often used as LCh(ab) in imaging software; LChuv is a related variant using the Luv space.

Limitations: While closer to perceptual uniformity than a/b, CIELCHab is not perfectly perceptually uniform and depends on the underlying Lab representation, which itself is device-independent but not perfect; results depend on illuminant and observer model.