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;
}));