var scene = new THREE.Scene();
var camera = new THREE.PerspectiveCamera(
  75,
  window.innerWidth / window.innerHeight,
  0.1,
  1000
);
var renderer = new THREE.WebGLRenderer();

renderer.setClearColor(0xffffff);
renderer.setSize(window.innerWidth, window.innerHeight);

document.body.appendChild(renderer.domElement);

ballRadius = 1;
ballHeight = 8; // of the center
ballBouncePeriod = 3; //in whatever units Time is measured in
maxBallHeight = 8; // of the center

time = 0;
deltaT = 0.035;

var ballMat = new THREE.MeshNormalMaterial();
var ballG = new THREE.SphereGeometry(ballRadius, 30, 30);

var ball = new THREE.Mesh(ballG, ballMat);

function linearMap(x, minx, maxx, miny, maxy) {
  //Transforms x from [minx,maxx] to y in [miny,maxy]
  //t is in [0,1]
  t = (x - minx) / (maxx - minx);
  y = t * (maxy - miny) + miny;
  return y;
}

function updatePosition() {
  time += deltaT;
  //rescale the Time dimension so that P, the period of bouncing, maps to pi
  angle = (time * Math.PI) / ballBouncePeriod;
  abs_cos = Math.abs(Math.cos(angle));
  ballHeight = linearMap(abs_cos, 0, 1, ballRadius, maxBallHeight);
  return ballHeight;
}

scene.add(ball);

camera.position.z = 30;

var controls = new THREE.OrbitControls(camera, renderer.domElement);

function render() {
  console.log(updatePosition());
  ball.position.y = updatePosition();
  requestAnimationFrame(render);
  renderer.render(scene, camera);
}

render();