bracketing: Angular Bracketing Decomposition

Directional vector decomposition for smooth angular interpolation

The bracketing functions decompose a directional vector into two adjacent angular axes with a blend factor. Given direction vector $\vec{d}$, the system computes:

$$\text{angle} = \text{atan2}(d_y, d_x) + 2\pi$$ $$\text{fractional} = \text{angle} \bmod \Delta\theta$$

Where $\Delta\theta = \frac{\pi}{20}$ represents the angular discretization step.

Angular Quantization Analysis

Function	Output	Description
bracketingAxis0	vec2	First quantized axis vector
bracketingAxis1	vec2	Adjacent quantized axis vector
bracketingBlend	float	Interpolation factor $[0,1]$

Directional Field Visualization

ライブエディター

const fragment = () => {
      const center = uv.sub(0.5).mul(2)
      const len = center.length()
      const safeCenter = center.div(max(len, 0.001))
      const axis0 = bracketingAxis0(safeCenter)
      const intensity = axis0.x.mul(0.5).add(0.5)
      return vec4(vec3(intensity), 1)
}