linear2gamma: Linear to Gamma Space Display Conversion

Inverse Power Function Display Mathematics

Linear to gamma conversion transforms mathematically linear color values to display-optimized gamma space using inverse power function $v^{1/\gamma}$ where $1/\gamma = 1/2.2 ≈ 0.4545$ compensates for display device response curves.

The mathematical transformation applies:

$G = L^{1/\gamma}$

Where $L$ represents linear luminance input and $G$ the gamma-corrected display output. This inverse transformation ensures proper luminance distribution on cathode-ray tube displays and maintains perceptual uniformity across brightness levels.

Display gamma correction compresses linear light values into perceptually uniform distribution matching human visual response characteristics.

Live Editor

const fragment = () => {
      const strips = uv.y.mul(12).floor()
      const linear_input = uv.x.pow(3)
      const gamma_output = linear2gamma(linear_input)
      const comparison = linear_input.select(gamma_output, strips.mod(2).equal(0))
      return vec4(vec3(comparison), 1)
}

Live Editor

const fragment = () => {
      const cellular = uv.mul(6).floor()
      const cell_id = cellular.x.add(cellular.y.mul(6))
      const linear_base = cell_id.div(36).pow(2)
      const gamma_corrected = linear2gamma(linear_base)
      const temporal_mod = iTime.mul(4).add(cell_id).sin().mul(0.2).add(0.8)
      const result = gamma_corrected.mul(temporal_mod)
      return vec4(vec3(result), 1)
}

The linear to gamma transformation prepares computationally linear color values for display output. Dark regions receive compression while bright areas expand, creating perceptually uniform brightness distribution on gamma-corrected display devices.

This mathematical conversion bridges the gap between linear color computation and display technology requirements, ensuring accurate color reproduction and maintaining visual consistency across different display systems and viewing conditions.