cornu.md

Cornu Spiral

Code:

fresnelC(t) {
    let sum = 0;
    let n = 50;
    let dt = t / n;
    for (let i = 0; i < n; i++) {
      let u = i * dt;
      sum += cos((u * u) / 2) * dt;
    }
    return sum;
}

fresnelS(t) {
    let sum = 0;
    let n = 50;
    let dt = t / n;
    for (let i = 0; i < n; i++) {
      let u = i * dt;
      sum += sin((u * u) / 2) * dt;
    }
    return sum;
}

cornuSpiral() {
    let numPoints = 200;
    let maxT = this.a * PI;
    for (let i = 0; i < numPoints; i++) {
      let t = map(i, 0, numPoints, -maxT, maxT);
      let x = this.n + this.r * this.fresnelC(t);
      let y = this.n + this.r * this.fresnelS(t);
      this.points.push(createVector(x, y));
    }
}

Sources:

• Mathcurve - cornu spiral
• Virtual Math Museum - clothoid

🌄 Gallery

Recursive circles with cornu spiral	Rounded Star with cornu spiral
Square skierpinski with cornu spiral	Hilbert curve with cornu spiral