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bezier-easing

Bezier Curve based easing functions for Javascript animations

Dieses Skript sollte nicht direkt installiert werden. Es handelt sich hier um eine Bibliothek für andere Skripte, welche über folgenden Befehl in den Metadaten eines Skriptes eingebunden wird // @require https://update.greatest.deepsurf.us/scripts/7108/29098/bezier-easing.js 

// ==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;

}));