starSDF: Parametric Star Distance Field

Multi-Pointed Star Generation with Angular Precision

The starSDF function generates star-shaped distance fields with precise angular control. This function creates star polygons by dividing angular space into segments and applying alternating radius modulation to create the characteristic pointed and indented star geometry.

Mathematical Foundation

The star pattern is constructed through angular segmentation and polar transformation:

$$\theta_{seg} = \left\lfloor \frac{\theta \cdot V}{2\pi} \right\rfloor + 0.5$$ $$\theta_{star} = \frac{\theta_{seg}}{V} + \text{mix}(s, -s, \text{step}(0.5, \text{fract}(\theta \cdot V / 2\pi))) \cdot 2\pi$$ $$d_{star} = |\vec{r} \cdot (\cos(\theta_{star}), \sin(\theta_{star}))|$$

where $V$ represents the number of star points and $s$ controls the inner scaling factor.

Function Signatures

Function	Parameters	Description
starSDF(st, V, s)	vec2, int, float	Full control with custom inner scaling
starSDF(st, V)	vec2, int	Simplified version with default scaling

Parameters

Parameter	Type	Description
st	vec2	2D coordinate position
V	int	Number of star points (vertices)
s	float	Inner scaling factor (default: 0.1)

Implementation Demonstrations

ライブエディター

const fragment = () => {
      const vertices = iTime.sin().add(3).floor().toInt()
      const scale = iTime.cos().mul(0.3).add(3)
      const dist = starSDF(uv, vertices, scale)
      const brightness = float(0.1).smoothstep(0, dist).mul(0.9)
      const color = brightness.mul(vec3(1, 0.7, 0.3))
      return vec4(color, 1)
}