Anti-Aliased Mirror Function

Function Overview

The aamirror function creates a mirrored pattern that automatically applies anti-aliasing to eliminate visual artifacts. This function transforms input values into smooth, symmetric waves that repeat with perfect mirroring.

Mathematical Foundation

The anti-aliased mirror function creates symmetric patterns through mathematical transformation and filtering:

$v = \left| x - \lfloor x + 0.5 \rfloor \right| \cdot 2$

The anti-aliasing width calculation: $\text{afwidth} = \left\|\frac{d}{dx}(x), \frac{d}{dy}(x)\right\|$

The result is processed through Nyquist filtering for smooth transitions: $\text{aamirror}(x) = \text{nyquist}(v, \text{afwidth})$

Where the Nyquist filter applies: $\text{nyquist}(v, w) = \text{smoothstep}(0, w, v)$

This creates perfect mirror symmetry with automatic anti-aliasing that adapts to screen pixel density.

Core Implementation Logic

Component	Purpose	Mathematical Expression
Mirror Transform	Creates symmetric pattern	abs(x - floor(x + 0.5)) * 2
Anti-aliasing Width	Calculates smoothing factor	vec2(dFdx(x), dFdy(x)).length()
Nyquist Filter	Prevents aliasing artifacts	mix(0.5, pattern, smoothstep(...))

Basic Mirror Pattern

Create fundamental mirrored waves that repeat seamlessly across space.

ライブエディター

const fragment = () => {
      const x = uv.x.mul(8)
      const mirror = aamirror(x)
      const color = vec3(mirror)
      return vec4(color, 1)
}

Distorted Mirror Field

Apply spatial distortions to mirror patterns for organic, fluid effects.

ライブエディター

const fragment = () => {
      const distortion = uv.y.mul(8).sin().mul(0.3)
      const x = uv.x.mul(6).add(distortion)
      const mirror = aamirror(x)
      const intensity = mirror.pow(2)
      const color = vec3(intensity.mul(0.9).add(0.1))
      return vec4(color, 1)
}