getBezierCurvePoints.js

function getPointAlongALine(p0, p1, t) {
  return Math.round(((1 - t) * p0 + (t * p1)) * 10) / 10;
}

function reduce(points, t) {

  if (points.length === 1) {
    return points;
  }

  const reducedPoints = [];

  for (let i = 1; i < points.length; i++) {

    const p0 = points[i - 1];
    const p1 = points[i];

    const px = getPointAlongALine(p0.x, p1.x, t);
    const py = getPointAlongALine(p0.y, p1.y, t);

    reducedPoints.push({x: px, y: py});
  }

  return reduce(reducedPoints, t);
}

function getBezierCurvePoints(p0, c0, c1, p1) {
  const result = [];
  for (let t = 0; t <= 1; t += 0.1) {
    result.push(reduce([p0, c0, c1, p1], t));
  }
  return result;
}

const result = getBezierCurvePoints(
  {x: 0, y: 5},
  {x: 2, y: 8},
  {x: 8, y: 8},
  {x: 10, y: 5}
);

console.log('result', result);