bezier-easing

Bezier Curve based easing functions for Javascript animations
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// ==UserScript==
// @name        bezier-easing
// @version     0.4.4
// @description Bezier Curve based easing functions for Javascript animations
// @license		MIT (https://github.com/gre/bezier-easing/blob/master/LICENSE)
// ==/UserScript==

/**
 * BezierEasing - use bezier curve for transition easing function
 * by Gaëtan Renaudeau 2014 – MIT License
 *
 * Credits: is based on Firefox's nsSMILKeySpline.cpp
 * Usage:
 * var spline = BezierEasing(0.25, 0.1, 0.25, 1.0)
 * spline(x) => returns the easing value | x must be in [0, 1] range
 *
 */
(function (definition) {
  if (typeof exports === "object") {
    module.exports = definition();
  } else if (typeof define === 'function' && define.amd) {
    define([], definition);
  } else {
    window.BezierEasing = definition();
  }
}(function () {
  var global = this;

  // These values are established by empiricism with tests (tradeoff: performance VS precision)
  var NEWTON_ITERATIONS = 4;
  var NEWTON_MIN_SLOPE = 0.001;
  var SUBDIVISION_PRECISION = 0.0000001;
  var SUBDIVISION_MAX_ITERATIONS = 10;

  var kSplineTableSize = 11;
  var kSampleStepSize = 1.0 / (kSplineTableSize - 1.0);

  var float32ArraySupported = 'Float32Array' in global;

  function BezierEasing (mX1, mY1, mX2, mY2) {
    // Validate arguments
    if (arguments.length !== 4) {
      throw new Error("BezierEasing requires 4 arguments.");
    }
    for (var i=0; i<4; ++i) {
      if (typeof arguments[i] !== "number" || isNaN(arguments[i]) || !isFinite(arguments[i])) {
        throw new Error("BezierEasing arguments should be integers.");
      } 
    }
    if (mX1 < 0 || mX1 > 1 || mX2 < 0 || mX2 > 1) {
      throw new Error("BezierEasing x values must be in [0, 1] range.");
    }

    var mSampleValues = float32ArraySupported ? new Float32Array(kSplineTableSize) : new Array(kSplineTableSize);
   
    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 newtonRaphsonIterate (aX, aGuessT) {
      for (var i = 0; i < NEWTON_ITERATIONS; ++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;
    }

    function calcSampleValues () {
      for (var i = 0; i < kSplineTableSize; ++i) {
        mSampleValues[i] = calcBezier(i * kSampleStepSize, mX1, mX2);
      }
    }

    function binarySubdivide (aX, aA, aB) {
      var currentX, currentT, i = 0;
      do {
        currentT = aA + (aB - aA) / 2.0;
        currentX = calcBezier(currentT, mX1, mX2) - aX;
        if (currentX > 0.0) {
          aB = currentT;
        } else {
          aA = currentT;
        }
      } while (Math.abs(currentX) > SUBDIVISION_PRECISION && ++i < SUBDIVISION_MAX_ITERATIONS);
      return currentT;
    }

    function getTForX (aX) {
      var intervalStart = 0.0;
      var currentSample = 1;
      var lastSample = kSplineTableSize - 1;

      for (; currentSample != lastSample && mSampleValues[currentSample] <= aX; ++currentSample) {
        intervalStart += kSampleStepSize;
      }
      --currentSample;

      // Interpolate to provide an initial guess for t
      var dist = (aX - mSampleValues[currentSample]) / (mSampleValues[currentSample+1] - mSampleValues[currentSample]);
      var guessForT = intervalStart + dist * kSampleStepSize;

      var initialSlope = getSlope(guessForT, mX1, mX2);
      if (initialSlope >= NEWTON_MIN_SLOPE) {
        return newtonRaphsonIterate(aX, guessForT);
      } else if (initialSlope === 0.0) {
        return guessForT;
      } else {
        return binarySubdivide(aX, intervalStart, intervalStart + kSampleStepSize);
      }
    }

    var _precomputed = false;
    function precompute() {
      _precomputed = true;
      if (mX1 != mY1 || mX2 != mY2)
        calcSampleValues();
    }

    var f = function (aX) {
      if (!_precomputed) precompute();
      if (mX1 === mY1 && mX2 === mY2) return aX; // linear
      // Because JavaScript number are imprecise, we should guarantee the extremes are right.
      if (aX === 0) return 0;
      if (aX === 1) return 1;
      return calcBezier(getTForX(aX), mY1, mY2);
    };

    f.getControlPoints = function() { return [{ x: mX1, y: mY1 }, { x: mX2, y: mY2 }]; };

    var args = [mX1, mY1, mX2, mY2];
    var str = "BezierEasing("+args+")";
    f.toString = function () { return str; };

    var css = "cubic-bezier("+args+")";
    f.toCSS = function () { return css; };

    return f;
  }

  // CSS mapping
  BezierEasing.css = {
    "ease":        BezierEasing(0.25, 0.1, 0.25, 1.0),
    "linear":      BezierEasing(0.00, 0.0, 1.00, 1.0),
    "ease-in":     BezierEasing(0.42, 0.0, 1.00, 1.0),
    "ease-out":    BezierEasing(0.00, 0.0, 0.58, 1.0),
    "ease-in-out": BezierEasing(0.42, 0.0, 0.58, 1.0)
  };

  return BezierEasing;

}));