crossSDF: Cross-Shaped Distance Field Composition

Geometric Intersection of Perpendicular Rectangles

The crossSDF function generates a cross-shaped signed distance field by computing the minimum distance between two perpendicular rectangular strips. This composite primitive demonstrates SDF combination techniques through geometric intersection.

Mathematical Foundation

The cross SDF operates through rectangular composition and minimum distance selection:

$$d_{\text{cross}}(st, s) = \min(d_{\text{rect}}(st, (0.25, s)), d_{\text{rect}}(st, (s, 0.25)))$$

where the cross is formed by intersecting:

• Vertical rectangle: width = 0.25, height = $s$
• Horizontal rectangle: width = $s$, height = 0.25

The minimum function selects the closest distance from either rectangular component.

Function Signature

Parameter	Type	Description
st	vec2	Sample point coordinates
s	float	Cross arm length parameter

Implementation Demonstrations

ライブエディター

const fragment = () => {
      const dist = crossSDF(uv, iTime.sin().mul(0.5).add(0.5))
      const inside = dist.step(0.5)
      const edge = float(0.02).smoothstep(0, dist.abs())
      const color = inside.mul(0.7).add(edge.mul(0.4))
      return vec4(color.mul(vec3(1, 0.3, 0.5)), 1)
}