hexSDF: Regular Hexagon Distance Field

Six-Sided Polygon Geometry in Two Dimensions

The hexSDF function generates a signed distance field for a regular hexagon. This function transforms input coordinates to a normalized space and computes distance using hexagonal symmetry properties.

Mathematical Foundation

The hexagon distance field utilizes geometric symmetry principles:

$$d_{\text{hex}} = \max(|y|, \frac{\sqrt{3}}{2} x + \frac{1}{2} y)$$

where the input coordinates are first normalized to the range $[-1, 1]$ and then made absolute to exploit the hexagon's symmetry.

The coefficient $\frac{\sqrt{3}}{2} \approx 0.866025$ represents the geometric relationship in a regular hexagon where:

• The angle between adjacent sides is $120°$
• The slope of hexagon edges creates this specific ratio

Function Signature

Parameter	Type	Description
st	vec2	2D coordinate position (typically UV coordinates)

Implementation Demonstrations

ライブエディター

const fragment = () => {
      const pos = uv.sub(0.5).mul(2)
      const dist = hexSDF(pos.add(0.5))
      const inside = dist.step(1)
      const edge = float(0.05).smoothstep(0, dist.sub(1).abs())
      const color = inside.mul(0.8).add(edge.mul(0.6))
      return vec4(color.mul(vec3(0.3, 0.7, 1)), 1)
}