nearest: Nearest Neighbor Quantization

Coordinate Discretization and Pixelation

The nearest function quantizes continuous coordinates to discrete grid positions, creating pixelation effects and nearest-neighbor sampling patterns. This transformation maps smooth coordinates to the nearest grid points at a specified resolution.

Mathematical Foundation

The quantization formula applies discrete sampling with offset correction:

$$\text{nearest}(v, r) = \frac{\lfloor v \cdot r \rfloor}{r} + \frac{0.5}{r - 1}$$

Where:

• $v$ = input coordinates [0,1]
• $r$ = resolution vector (grid dimensions)
• The offset term centers samples within grid cells

ライブエディター

const fragment = () => {
      const pixelated = nearest(uv, vec2(16, 12))
      const pattern = sin(pixelated.x.mul(iTime)).mul(cos(pixelated.y.mul(iTime)))
      const color = pattern.mul(0.5).add(0.5)
      return vec4(vec3(color), 1)
}