Add bounce effect to Effect.Transitions

[edg2s]

To simulate an object under constant force (e.g. gravity) hitting a surface with a constant coefficient of restitution. The function I've defined below is a function generating function, which takes two parameters: the number of bounces and the coefficient of restitution (called "decay"). A number of pre-calculations are performed to improve the performance of the actual transition function.

bounce: function(bounces, decay) {
  // default values
  if(decay == null) decay = 1/3;
  if(bounces == null) bounces = 2;

  // solve geometric series to calculate speed
  var rootd = Math.sqrt(decay);
  var rootdn = Math.sqrt(Math.pow(decay, bounces));
  var f = Math.pow((1 + rootd - (2 * rootdn)) / (1 - rootd), 2);

  // pre-calculate offsets
  var offsets = [];
  var offset = 0;
  var apex = 1;
  for(var b = 0; b < bounces; b++) {
    offsets.push(offset)
    offset += Math.sqrt(apex / f);
    apex *= decay;
    offset += Math.sqrt(apex / f);
  }

  // generate the bounce function
  return (function (pos) {
    var h = 0;
    var apex = 1;
    for(var b = 0; b < bounces; b++) {
      h = Math.max(h, apex - (f * Math.pow(pos - offsets[b], 2)));
      apex *= decay;
    }
    return 1 - h;
  });
},

Usage:
transition: Effect.Transitions.bounce() // use default values of 5, 1/3
or
transition: Effect.Transitions.bounce(3) // 3 bounces, default decay (1/3)
or
transition: Effect.Transitions.bounce(4, 1/2) // 4 bounces, decay 1/2

[madrobby]

Sweet stuff. I'll add that in scripty2.