JSFiddle - React, Tailwind, and code Playground

HTML

<body>
	<canvas id="canvas"></canvas>
	<svg>
		<path fill="none" d="M100,100 a45,35 -30 0,1 50,-25" stroke="red" stroke-width="2"></path>
	</svg>
</body>

CSS

html, body {
  height: 100%;
  margin: 0;
  padding: 0;
}

svg, canvas {
  height: 100%;
  width: 100%;
  position: absolute;
  left:0;
  top:0;
}
svg {
  opacity:0.5;
}

JavaScript

var canvas = document.getElementById("canvas");
var ctx = canvas.getContext("2d");

// M100,350
// a45,35 -30 0,1 50,-25

canvas.width = document.body.clientWidth;
canvas.height = document.body.clientHeight;
ctx.strokeWidth = 2;
ctx.strokeStyle = "#000000";
function clamp(value, min, max) {
  return Math.min(Math.max(value, min), max)
}

function svgAngle(ux, uy, vx, vy ) {
  var dot = ux*vx + uy*vy;
  var len = Math.sqrt(ux*ux + uy*uy) * Math.sqrt(vx*vx + vy*vy);

  var ang = Math.acos( clamp(dot / len,-1,1) );
  if ( (ux*vy - uy*vx) < 0)
    ang = -ang;
  return ang;
}

function generateBezierPoints(rx, ry, phi, flagA, flagS, x1, y1, x2, y2) {
  var rX = Math.abs(rx);
  var rY = Math.abs(ry);

  var dx2 = (x1 - x2)/2;
  var dy2 = (y1 - y2)/2;

  var x1p =  Math.cos(phi)*dx2 + Math.sin(phi)*dy2;
  var y1p = -Math.sin(phi)*dx2 + Math.cos(phi)*dy2;

  var rxs = rX * rX;
  var rys = rY * rY;
  var x1ps = x1p * x1p;
  var y1ps = y1p * y1p;

  var cr = x1ps/rxs + y1ps/rys;
  if (cr > 1) {
    var s = Math.sqrt(cr);
    rX = s * rX;
    rY = s * rY;
    rxs = rX * rX;
    rys = rY * rY;
  }

  var dq = (rxs * y1ps + rys * x1ps);
  var pq = (rxs*rys - dq) / dq;
  var q = Math.sqrt( Math.max(0,pq) );
  if (flagA === flagS)
    q = -q;
  var cxp = q * rX * y1p / rY;
  var cyp = - q * rY * x1p / rX;

  var cx = Math.cos(phi)*cxp - Math.sin(phi)*cyp + (x1 + x2)/2;
  var cy = Math.sin(phi)*cxp + Math.cos(phi)*cyp + (y1 + y2)/2;

  var theta = svgAngle( 1,0, (x1p-cxp) / rX, (y1p - cyp)/rY );

  var delta = svgAngle(
    (x1p - cxp)/rX, (y1p - cyp)/rY,
    (-x1p - cxp)/rX, (-y1p-cyp)/rY);

  delta = delta - Math.PI * 2 * Math.floor(delta / (Math.PI * 2));

  if (!flagS)
    delta -= 2 * Math.PI;

  var n1 = theta, n2 = delta;


  // E(n)
  // cx +acosθcosη−bsinθsinη
  // cy +asinθcosη+bcosθsinη
  function E(n) {
    var enx = cx + rx * Math.cos(phi) * Math.cos(n) - ry * Math.sin(phi) * Math.sin(n);
    var eny = cy + rx * Math.sin(phi) * Math.cos(n) + ry * Math.cos(phi) *...