// https://virtualmathmuseum.org/Curves/clothoid/kappaCurve.html

​

​

class CornuSpiral {

  constructor(n, maxSpirals, r, angle) {

    this.n = n;

    this.maxSp = maxSpirals;

    this.r = r;

    this.m = 50;

    this.angle = angle;

    this.points = [];

  }

​

  calculatePoints() {

    for (let i = 0; i < this.n; i++) {

      let t = map(i, 0, this.n, -this.maxSp, this.maxSp);

      let x = this.r * this.fresnelC(t);

      let y = this.r * this.fresnelS(t);

      this.points.push(createVector(x, y));

    }

  }

​

  fresnelC(t) {

    let sum = 0;

    let dt = t / this.m;

    for (let i = 0; i < this.m; i++) {

      let u = i * dt;

      sum += cos(u * u / 2) * dt;

    }

    return sum;

  }

​

  fresnelS(t) {

    let sum = 0;

    let dt = t / this.m;

    for (let i = 0; i < this.m; i++) {

      let u = i * dt;

      sum += sin(u * u /2 ) * dt;

    }

    return sum;

  }

​

  show(x, y) {

    push();

    translate(x, y);

    rotate(this.angle);

    stroke(255);

    strokeWeight(1.2);

    noFill();

    beginShape();

    for (let p of this.points) {

      vertex(p.x, p.y);

    }

    endShape();

    pop();

  }

}

​