Lomiri
KeySpline.js
1 /** MIT License
2  *
3  * KeySpline - use bezier curve for transition easing function
4  * Copyright (c) 2012 Gaetan Renaudeau <renaudeau.gaetan@gmail.com>
5  *
6  * Permission is hereby granted, free of charge, to any person obtaining a
7  * copy of this software and associated documentation files (the "Software"),
8  * to deal in the Software without restriction, including without limitation
9  * the rights to use, copy, modify, merge, publish, distribute, sublicense,
10  * and/or sell copies of the Software, and to permit persons to whom the
11  * Software is furnished to do so, subject to the following conditions:
12  *
13  * The above copyright notice and this permission notice shall be included in
14  * all copies or substantial portions of the Software.
15  *
16  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
17  * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
18  * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
19  * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
20  * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
21  * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
22  * DEALINGS IN THE SOFTWARE.
23  */
24 /**
25 * KeySpline - use bezier curve for transition easing function
26 * is inspired from Firefox's nsSMILKeySpline.cpp
27 * Usage:
28 * var spline = new KeySpline(0.25, 0.1, 0.25, 1.0)
29 * spline.get(x) => returns the easing value | x must be in [0, 1] range
30 */
31 
32 .pragma library
33 
34 function keySpline (mX1, mY1, mX2, mY2) {
35 
36  this.get = function(aX) {
37  if (mX1 == mY1 && mX2 == mY2) return aX; // linear
38  return CalcBezier(GetTForX(aX), mY1, mY2);
39  }
40 
41  function A(aA1, aA2) { return 1.0 - 3.0 * aA2 + 3.0 * aA1; }
42  function B(aA1, aA2) { return 3.0 * aA2 - 6.0 * aA1; }
43  function C(aA1) { return 3.0 * aA1; }
44 
45  // Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2.
46  function CalcBezier(aT, aA1, aA2) {
47  return ((A(aA1, aA2)*aT + B(aA1, aA2))*aT + C(aA1))*aT;
48  }
49 
50  // Returns dx/dt given t, x1, and x2, or dy/dt given t, y1, and y2.
51  function GetSlope(aT, aA1, aA2) {
52  return 3.0 * A(aA1, aA2)*aT*aT + 2.0 * B(aA1, aA2) * aT + C(aA1);
53  }
54 
55  function GetTForX(aX) {
56  // Newton raphson iteration
57  var aGuessT = aX;
58  for (var i = 0; i < 4; ++i) {
59  var currentSlope = GetSlope(aGuessT, mX1, mX2);
60  if (currentSlope == 0.0) return aGuessT;
61  var currentX = CalcBezier(aGuessT, mX1, mX2) - aX;
62  aGuessT -= currentX / currentSlope;
63  }
64  return aGuessT;
65  }
66 }