Convert a Circle shape to a set of Bezier curves (SVG Path string) using Javascript

circleToBezier.js

export default function circleToBezier(cx, cy, r) {
  // Inspired by https://codereview.stackexchange.com/questions/141491/calculating-a-circle-with-bezier-curves

  function Coord(x, y) {
      var self = this;

      this.x = parseFloat(x);
      this.y = parseFloat(y);

      this.offset = function(offsetX, offsetY) {
          self.x += offsetX;
          self.y += offsetY;
      }
  }

  Coord.prototype.toString = function () {
      return `${this.x} ${this.y}`
  }

  function BezierCurve(x, y, c1, c2) {
      var self = this;

      this.x = x;
      this.y = y;
      this.c1 = c1;
      this.c2 = c2;

      this.offset = function(offsetX, offsetY) {
          self.x += offsetX;
          self.y += offsetY;

          self.c1.offset(offsetX, offsetY);
          self.c2.offset(offsetX, offsetY);
      }
  }

  BezierCurve.prototype.toString = function () {
      return `${this.c1.toString()} ${this.c2.toString()} ${this.x} ${this.y}`
  }

  var BEZIER_CONTROL_POINT = 0.552284749831;

  var twoR = r * 2;
  var offsetX = cx - r;
  var offsetY = cy - r;
  var controlPointOffset = r * BEZIER_CONTROL_POINT;


  // from Middle Left
  var firstMove = new Coord(0, r);

  // curve to Top Middle
  var curve1 = new BezierCurve(r, 0, 
                      new Coord(0, r - controlPointOffset),
                      new Coord(r - controlPointOffset, 0));

  // curve to Middle Right
  var curve2 = new BezierCurve(twoR, r,
                      new Coord(r + controlPointOffset, 0),
                      new Coord(twoR, r - controlPointOffset));

  // curve to Bottom Middle
  var curve3 = new BezierCurve(r, twoR,
                      new Coord(twoR, r + controlPointOffset),
                      new Coord(r + controlPointOffset, twoR));

  // curve back to Middle Left
  var curve4 = new BezierCurve(0, r,
                      new Coord(r - controlPointOffset, twoR),
                      new Coord(0, r + controlPointOffset));

  if (offsetX > 0) {

      firstMove.offset(offsetX, offsetY);
      curve1.offset(offsetX, offsetY);
      curve2.offset(offsetX, offsetY);
      curve3.offset(offsetX, offsetY);
      curve4.offset(offsetX, offsetY);
  }

  let output = '';
  output += (`M ${firstMove.toString()}`);
  output += (`C ${curve1.toString()}`);
  output += (`C ${curve2.toString()}`);
  output += (`C ${curve3.toString()}`);
  output += (`C ${curve4.toString()}`);
  output += ("Z");

  return output;
}