player/js/3rd_party/BezierEaser.js

var BezierFactory = (function(){
    /**
     * BezierEasing - use bezier curve for transition easing function
     * by Gaëtan Renaudeau 2014 - 2015 – MIT License
     *
     * Credits: is based on Firefox's nsSMILKeySpline.cpp
     * Usage:
     * var spline = BezierEasing([ 0.25, 0.1, 0.25, 1.0 ])
     * spline.get(x) => returns the easing value | x must be in [0, 1] range
     *
     */

        var ob = {};
    ob.getBezierEasing = getBezierEasing;
    var beziers = {};

    function getBezierEasing(a,b,c,d,nm){
        var str = nm || ('bez_' + a+'_'+b+'_'+c+'_'+d).replace(/\./g, 'p');
        if(beziers[str]){
            return beziers[str];
        }
        var bezEasing = new BezierEasing([a,b,c,d]);
        beziers[str] = bezEasing;
        return bezEasing;
    }

// 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 = typeof Float32Array === 'function';

    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 binarySubdivide (aX, aA, aB, mX1, mX2) {
        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 newtonRaphsonIterate (aX, aGuessT, mX1, mX2) {
        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;
    }

    /**
     * points is an array of [ mX1, mY1, mX2, mY2 ]
     */
    function BezierEasing (points) {
        this._p = points;
        this._mSampleValues = float32ArraySupported ? new Float32Array(kSplineTableSize) : new Array(kSplineTableSize);
        this._precomputed = false;

        this.get = this.get.bind(this);
    }

    BezierEasing.prototype = {

        get: function (x) {
            var mX1 = this._p[0],
                mY1 = this._p[1],
                mX2 = this._p[2],
                mY2 = this._p[3];
            if (!this._precomputed) this._precompute();
            if (mX1 === mY1 && mX2 === mY2) return x; // linear
            // Because JavaScript number are imprecise, we should guarantee the extremes are right.
            if (x === 0) return 0;
            if (x === 1) return 1;
            return calcBezier(this._getTForX(x), mY1, mY2);
        },

        // Private part

        _precompute: function () {
            var mX1 = this._p[0],
                mY1 = this._p[1],
                mX2 = this._p[2],
                mY2 = this._p[3];
            this._precomputed = true;
            if (mX1 !== mY1 || mX2 !== mY2)
                this._calcSampleValues();
        },

        _calcSampleValues: function () {
            var mX1 = this._p[0],
                mX2 = this._p[2];
            for (var i = 0; i < kSplineTableSize; ++i) {
                this._mSampleValues[i] = calcBezier(i * kSampleStepSize, mX1, mX2);
            }
        },

        /**
         * getTForX chose the fastest heuristic to determine the percentage value precisely from a given X projection.
         */
        _getTForX: function (aX) {
            var mX1 = this._p[0],
                mX2 = this._p[2],
                mSampleValues = this._mSampleValues;

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

    return ob;

}());