blendDarken: Selective Minimum Blending

Mathematical Foundation of Darkening

Darken blending implements a simple comparison operation that selects the minimum value between base and blend colors for each channel. This creates natural shadow effects by preserving darker tones while allowing lighter areas to show through.

The mathematical definition is:

$$C_{result} = \min(C_{base}, C_{blend})$$

This component-wise minimum operation ensures that only darker values contribute to the final result, creating natural shadowing without complex mathematical transformations.

Selective Darkening Properties

Property	Description	Mathematical Expression
Component Independence	Each RGB channel processed separately	$R = \min(R_1, R_2)$
Monotonic Darkening	Result never brighter than inputs	$C_{result} \leq \min(C_1, C_2)$
Identity Preservation	White blend leaves base unchanged	$\min(C, 1) = C$
Symmetric Operation	Order independence	$\min(A, B) = \min(B, A)$

Live Editor

const fragment = () => {
      const base = vec3(0.8, 0.9, 0.7).mul(
              float(0.2).smoothstep(0.8, uv.sub(vec2(0.5)).length())
      )
      const pattern1 = uv.x.mul(12).fract().step(0.5)
      const pattern2 = uv.y.mul(8).fract().step(0.5)
      const darken = vec3(
              pattern1.mul(0.6),
              pattern2.mul(0.4),
              pattern1.mul(pattern2).mul(0.3)
      )
      const result = blendDarkenVec3(base, darken)
      return vec4(result, 1)
}