Draw ellipse with bezierVertex() in p5.js

bezierEllipse.js

/*
* @param {Number} x x-coordinate for the ellipse
* @param {Number} y y-coordinate for the ellipse
* @param {Number} r radius of the ellipse
* @param {Number} n segements of the ellipse, defaults to 4
*/

p5.prototype.bezierEllipse(x, y, r, n) {
  // caulate length of each controls: r - (4/3)*tan(PI/(2n))
  var ctrl = r *  (4 / 3) * tan(PI / (2 * n));
  // translate to the center of circle: (x, y)
  push();
  translate(x, y);
  
  beginShape();
  vertex(r, 0);
  for(var i = 0; i < n; i ++) {
    var firstAngle = (PI * 2 / n) * i;
    var secondAngle = (PI * 2 / n) * (i + 1);
    var firstVtx = {x: cos(firstAngle) * r, y: -sin(firstAngle) * r};
    var secondVtx = {x: cos(secondAngle) * r, y: -sin(secondAngle) * r};
    var firstCtrl = {x: firstVtx.x - ctrl * sin(firstAngle), y: firstVtx.y - ctrl * cos(firstAngle)};
    var secondCtrl = {x: secondVtx.x + ctrl * sin(secondAngle), y: secondVtx.y + ctrl * cos(secondAngle)};
    drawBezierV(firstCtrl.x, firstCtrl.y, secondCtrl.x,secondCtrl.y, secondVtx.x, secondVtx.y);
  }
  noFill();
  endShape();
  pop();
}

// extends the original bezierVertex(), for visualize and debig purpose
function drawBezierV(x1, y1, x2, y2, x3, y3) {
  bezierVertex(x1, y1, x2, y2, x3, y3);
  fill('#4aff2e'); //marks two control point with light green
  ellipse(x1, y1, 5, 5);
  ellipse(x2, y2, 5, 5);
  fill('#ff2e2e'); // red
  rectMode(CENTER); //marks anchor point with red
  rect(x3, y3, 8, 8);
}