var shape = {};
shape.box = {};
shape.box.points = function (ll, ur) {
  return [ll, ll.add([ur.x - ll.x, 0]), ur, ll.add([0, ur.y - ll.y])];
};
shape.sphere = {};
shape.circle = {};
shape.sphere.volume = function (r) {
  return (Math.pi * r * r * r * 4) / 3;
};
shape.sphere.random = function (r, theta = [0, 1], phi = [-0.5, 0.5]) {
  if (typeof r === "number") r = [r, r];
  if (typeof theta === "number") theta = [theta, theta];
  if (typeof phi === "number") phi = [phi, phi];

  var ra = Math.random_range(r[0], r[1]);
  var ta = Math.turn2rad(Math.random_range(theta[0], theta[1]));
  var pa = Math.turn2rad(Math.random_range(phi[0], phi[1]));
  return [ra * Math.sin(ta) * Math.cos(pa), ra * Math.sin(ta) * Math.sin(pa), ra * Math.cos(ta)];
};

shape.circle.area = function (r) {
  return Math.pi * r * r;
};
shape.circle.random = function (r, theta) {
  return shape.sphere.random(r, theta).xz;
};

shape.box = function (w, h) {
  w /= 2;
  h /= 2;

  var points = [
    [w, h],
    [-w, h],
    [-w, -h],
    [w, -h],
  ];

  return points;
};

shape.ngon = function (radius, n) {
  return shape.arc(radius, 360, n);
};

shape.arc = function (radius, angle, n, start = 0) {
  start = Math.deg2rad(start);
  if (angle >= 360) angle = 360;

  if (n <= 1) return [];
  var points = [];

  angle = Math.deg2rad(angle);
  var arclen = angle / n;
  for (var i = 0; i < n; i++) points.push(Vector.rotate([radius, 0], start + arclen * i));

  return points;
};

shape.circle.points = function (radius, n) {
  if (n <= 1) return [];
  return shape.arc(radius, 360, n);
};

shape.corners2points = function (ll, ur) {
  return [ll, ll.add([ur.x, 0]), ur, ll.add([0, ur.y])];
};

return { shape };