mmax: Multi-Value Maximum Function

Component-wise Maximum Extraction

The mmax function finds the largest value among multiple inputs or vector components. It's a utility function that works with 2-4 individual values or extracts the maximum component from vec2, vec3, or vec4 vectors.

Mathematical Definition:

$\text{mmax}(\mathbf{v}) = \max\{v_1, v_2, v_3, v_4\}$

For 4-dimensional vector space analysis:

$\mathbf{v} \in \mathbb{R}^4 \Rightarrow \text{mmax}(\mathbf{v}) = v_i \text{ where } i = \arg\max_j v_j$

The supremacy function establishes order relationships:

$\forall \mathbf{v} \in \mathbb{R}^n: \text{mmax}(\mathbf{v}) \geq v_i \quad \forall i \in \{1,2,\ldots,n\}$

This function is useful for extracting the dominant component from color values, finding peak intensities in multi-channel data, or determining which axis has the largest influence in vector calculations.

ライブエディター

const fragment = () => {
  const t = iTime.mul(0.4)
  const p = uv.sub(0.5)

      const f1 = p.mul(3.2).add(t.mul(0.8))
      const f2 = p.mul(2.1).add(t.mul(1.3))
      const f3 = p.length().mul(4.7).add(t.mul(0.6))
      const f4 = p.x.add(p.y).mul(1.9).add(t.mul(2.1))

      const waves = vec4(f1.x.sin().mul(f1.y.cos()),
                        f2.x.cos().mul(f2.y.sin().mul(1.4)),
                        f3.mul(7).sin().mul(0.7),
                        f4.mul(2.3).cos().mul(1.1))

      const supremacy = mmax(waves)
      const dominance = supremacy.abs().pow(1.8)
      const resonance = p.length().mul(8).add(supremacy.mul(4)).sin().mul(dominance)

      return vec4(resonance.mul(vec3(1, 0.7, 0.4)), 1)

}