Change coordinate in 2D and 3D

CoordinateConverter.js

function carToPol(vec) {
  var r = Math.sqrt(vec.x * vec.x + vec.y * vec.y);
  var a = Math.atan2(vec.y, vec.x);
  return {
    r:r,
    a:a
  }
}

function polToCar (coor) {
  return {
    x: coor.r * Math.cos(coor.a),
    y: coor.r * Math.sin(coor.a)
  };
}

function carToCyl (vec) {
  var coor = carToPol(vec);
  coor.z = vec.z;
  return coor;
}

function cylToCar (coor) {
  var vec = polToCar(coor);
  vec.z = coor.z;
  return z;
}

function carToSphere (vec) {
  var r = Math.sqrt(vec.x*vec.x + vec.y*vec.y + vec.z * vec.z);
  var lon = Math.atan2(vec.y,vec.x);
  var lat = Math.acos(vec.y/r); 
  return {
    r:r,
    lat:lat,
    lon: lon
  }
}

function sphereToCar (coor) {
  return {
    x: Math.cos(coor.lon) * coor.r,
    y: Math.sin(coor.lon) * coor.r,
    z: Math.cos(coor.lat) * coor.r
  }
}