/** MIT License
 *
 * KeySpline - use bezier curve for transition easing function
 * Copyright (c) 2012 Gaetan Renaudeau <renaudeau.gaetan@gmail.com>
 *
 * Permission is hereby granted, free of charge, to any person obtaining a
 * copy of this software and associated documentation files (the "Software"),
 * to deal in the Software without restriction, including without limitation
 * the rights to use, copy, modify, merge, publish, distribute, sublicense,
 * and/or sell copies of the Software, and to permit persons to whom the
 * Software is furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
 * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
 * FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 * DEALINGS IN THE SOFTWARE.
 */
/**
* KeySpline - use bezier curve for transition easing function
* is inspired from Firefox's nsSMILKeySpline.cpp
* Usage:
* var spline = new KeySpline(0.25, 0.1, 0.25, 1.0)
* spline.get(x) => returns the easing value | x must be in [0, 1] range
*/

.pragma library

function keySpline (mX1, mY1, mX2, mY2) {

  this.get = function(aX) {
    if (mX1 == mY1 && mX2 == mY2) return aX; // linear
    return CalcBezier(GetTForX(aX), mY1, mY2);
  }

  function A(aA1, aA2) { return 1.0 - 3.0 * aA2 + 3.0 * aA1; }
  function B(aA1, aA2) { return 3.0 * aA2 - 6.0 * aA1; }
  function C(aA1)      { return 3.0 * aA1; }

  // Returns x(t) given t, x1, and x2, or y(t) given t, y1, and y2.
  function CalcBezier(aT, aA1, aA2) {
    return ((A(aA1, aA2)*aT + B(aA1, aA2))*aT + C(aA1))*aT;
  }

  // Returns dx/dt given t, x1, and x2, or dy/dt given t, y1, and y2.
  function GetSlope(aT, aA1, aA2) {
    return 3.0 * A(aA1, aA2)*aT*aT + 2.0 * B(aA1, aA2) * aT + C(aA1);
  }

  function GetTForX(aX) {
    // Newton raphson iteration
    var aGuessT = aX;
    for (var i = 0; i < 4; ++i) {
      var currentSlope = GetSlope(aGuessT, mX1, mX2);
      if (currentSlope == 0.0) return aGuessT;
      var currentX = CalcBezier(aGuessT, mX1, mX2) - aX;
      aGuessT -= currentX / currentSlope;
    }
    return aGuessT;
  }
}