lch2lab: Cylindrical to Cartesian Color Space Conversion

Mathematical Foundation of Cartesian Coordinate Reconstruction

LCH to LAB conversion transforms cylindrical color coordinates into Cartesian representation where polar chroma and hue values become rectangular a and b components while preserving lightness.

The mathematical transformation: $\text{LAB} = \begin{bmatrix} L \\ C \cos(H \cdot \frac{\pi}{180}) \\ C \sin(H \cdot \frac{\pi}{180}) \end{bmatrix}$

Where L remains unchanged, a-component equals chroma times cosine of hue angle, and b-component equals chroma times sine of hue angle.

Trigonometric Projection Properties

The conversion from cylindrical to Cartesian coordinates projects polar coordinates onto rectangular axes. The chroma value scales the unit circle, while the hue angle determines the direction of projection.

Mathematical characteristics:

• Trigonometric projection: Chroma scaled by cosine and sine of hue angle
• Radian conversion: Hue converted from degrees to radians using π/180
• Lightness preservation: L component passes through unchanged

ライブエディター

const fragment = () => {
      const lightness = 60
      const chroma = uv.x.mul(40)
      const hue = uv.y.mul(360)
      const lchColor = vec3(lightness, chroma, hue)
      const labColor = lch2lab(lchColor)
      return vec4(labColor.mul(0.01).add(0.5), 1)
}