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gre/easing.js

Last active Sep 27, 2020
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Simple Easing Functions in Javascript - see https://github.com/gre/bezier-easing
/*
* Easing Functions - inspired from http://gizma.com/easing/
* only considering the t value for the range [0, 1] => [0, 1]
*/
EasingFunctions = {
// no easing, no acceleration
linear: t => t,
// accelerating from zero velocity
easeInQuad: t => t*t,
// decelerating to zero velocity
easeOutQuad: t => t*(2-t),
// acceleration until halfway, then deceleration
easeInOutQuad: t => t<.5 ? 2*t*t : -1+(4-2*t)*t,
// accelerating from zero velocity
easeInCubic: t => t*t*t,
// decelerating to zero velocity
easeOutCubic: t => (--t)*t*t+1,
// acceleration until halfway, then deceleration
easeInOutCubic: t => t<.5 ? 4*t*t*t : (t-1)*(2*t-2)*(2*t-2)+1,
// accelerating from zero velocity
easeInQuart: t => t*t*t*t,
// decelerating to zero velocity
easeOutQuart: t => 1-(--t)*t*t*t,
// acceleration until halfway, then deceleration
easeInOutQuart: t => t<.5 ? 8*t*t*t*t : 1-8*(--t)*t*t*t,
// accelerating from zero velocity
easeInQuint: t => t*t*t*t*t,
// decelerating to zero velocity
easeOutQuint: t => 1+(--t)*t*t*t*t,
// acceleration until halfway, then deceleration
easeInOutQuint: t => t<.5 ? 16*t*t*t*t*t : 1+16*(--t)*t*t*t*t
}
@warpech

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@warpech warpech commented Jun 5, 2013

Amazing, thanks!

@yairEO

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@yairEO yairEO commented Aug 26, 2013

Awesome!!! where can I find more? I want more variety for my code here:
http://dropthebit.com/demos/pathAnimator/

Update: I've found this fantastic blog post: http://joshondesign.com/2013/03/01/improvedEasingEquations

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@jjwhite jjwhite commented Oct 25, 2013

These are great. Thanks!

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@gre gre commented Nov 25, 2013

@yairEO : basically you can make infinite number of easing with bezier curves, see http://greweb.me/2012/02/bezier-curve-based-easing-functions-from-concept-to-implementation/

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@tieTYT tieTYT commented Apr 23, 2014

Nice. What about things like bounce?

@clouddueling

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@clouddueling clouddueling commented May 6, 2014

Does anyone have an example of these in a jsfiddle?

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@gre gre commented May 10, 2014

Hi @clouddueling, not sure if you are looking for this static easing function or the bezier-easing one ( https://github.com/gre/bezier-easing )

I have a few examples for the bezier-easing one:

http://greweb.me/glsl-transition/example/

http://greweb.me/bezier-easing/example/

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@bapbin bapbin commented Apr 18, 2015

Awesome, thank you!

@liuda101

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@liuda101 liuda101 commented Aug 4, 2015

Awesome! Thank you!

@hvgeertruy

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@hvgeertruy hvgeertruy commented Aug 20, 2015

This works. Thanks!

@bjorn-ali-goransson

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@bjorn-ali-goransson bjorn-ali-goransson commented Sep 9, 2015

Suggestion:

  // acceleration until halfway, then deceleration
  easeInOutQuad: function (t) { return t<.5 ? 2*t*t : -1+2*(2-t)*t },

Makes for more consistent style of coding, IMO.

Also, here is "decelerate in, accelerate out" easing for quad:

  // deceleration until halfway, then acceleration
  easeOutInQuad: function (t) { return t<.5 ? EasingFunctions.easeOutQuad(2 * t) * 0.5 : EasingFunctions.easeInQuad((2 * (t - 0.5))) * 0.5 + 0.5 },

The whole document could be refactored with reusing its own easing functions instead of reimplementing itself repeatedly.

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@OrangeBacon OrangeBacon commented Nov 3, 2015

thanks 👍

@DenislavD

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@DenislavD DenislavD commented Dec 1, 2015

This is very helpful.. saved me a lot of time.

@AshCoolman

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@AshCoolman AshCoolman commented Jan 13, 2016

Thanks!

@AndrewRayCode

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@AndrewRayCode AndrewRayCode commented Mar 13, 2016

Thanks for this! Really don't like the --t syntax though. Makes it almost impossible to figure out the order of operations in the functions

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@AndrewRayCode AndrewRayCode commented Mar 13, 2016

I ES6-ified this and removed the t-- stuff, which most eslint configs don't like https://gist.github.com/DelvarWorld/940a4a549f9e4c2f262c

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@AndrewRayCode AndrewRayCode commented Apr 4, 2016

I just open sourced a library of these functions and quite a few others https://github.com/DelvarWorld/easing-utils

The source code is heavily cleaned up from this gist to avoid things like inline mutation of variables.

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@riccardolardi riccardolardi commented May 12, 2016

How to use different range, say 1000 to 2000 instead of 0 to 1?

@ghost

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@ghost ghost commented May 19, 2016

Awesome. tnx.

@alberto2000 just multiply your distance with return value.

@lindell

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@lindell lindell commented Jun 21, 2016

Made use of higher order functions to make a more general and more compact version.

EaseIn  = function(power){return function(t){return Math.pow(t, power)}};
EaseOut = function(power){return function(t){return 1 - Math.abs(Math.pow(t-1, power))}};
EaseInOut = function(power){return function(t){return t<.5 ? EaseIn(power)(t*2)/2 : EaseOut(power)(t*2 - 1)/2+0.5}}

So for example, to use EasingFunctions.easeInOutCubic, just write.

EaseInOut(3)(t)

To get a better understanding of how this is used, this is the same as the original gist from @gre

EasingFunctions = {
  linear: EaseInOut(1)
  easeInQuad: EaseIn(2),
  easeOutQuad: EaseOut(2),
  easeInOutQuad: EaseInOut(2),
  easeInCubic: EaseIn(3),
  easeOutCubic: EaseOut(3),
  easeInOutCubic: EaseInOut(3),
  easeInQuart: EaseIn(4),
  easeOutQuart: EaseOut(4),
  easeInOutQuart: EaseInOut(4),
  easeInQuint: EaseIn(5),
  easeOutQuint: EaseOut(5),
  easeInOutQuint: EaseInOut(5)
}
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@kandebonfim kandebonfim commented Aug 30, 2016

Awsome!

@IllusionSector

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@IllusionSector IllusionSector commented Sep 9, 2016

What's the simplest way I could implement it?
Thanks.

@lvnr

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@lvnr lvnr commented Sep 29, 2016

Thank you so much for this!

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@dht dht commented Oct 2, 2016

Very great

@ChristianFigueroa

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@ChristianFigueroa ChristianFigueroa commented Oct 7, 2016

Here's some elastic ones just for fun

elasticEasings = {
    // elastic bounce effect at the beginning
    easeInElastic: function (t) { return (.04 - .04 / t) * Math.sin(25 * t) + 1 },
    // elastic bounce effect at the end
    easeOutElastic: function (t) { return .04 * t / (--t) * Math.sin(25 * t) },
    // elastic bounce effect at the beginning and end
    easeInOutElastic: function (t) { return (t -= .5) < 0 ? (.02 + .01 / t) * Math.sin(50 * t) : (.02 - .01 / t) * Math.sin(50 * t) + 1 }
}
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@adiakritos adiakritos commented Oct 29, 2016

how do you use these?

@sambeevors

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@sambeevors sambeevors commented Nov 16, 2016

how do you use these?

You just pass t = which is a value between 0 and 1. 0 being the start of the animation, and 1 being the end.

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@Kerndog73 Kerndog73 commented Nov 18, 2016

Here's some sine eases

  easeInSin: function (t) {
    return 1 + Math.sin(Math.PI / 2 * t - Math.PI / 2);
  }
  easeOutSin : function (t) {
    return Math.sin(Math.PI / 2 * t);
  }
  easeInOutSin: function (t) {
    return (1 + Math.sin(Math.PI * t - Math.PI / 2)) / 2;
  }
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@bilibiliou bilibiliou commented Jan 24, 2017

AweSome ! thank you save my life~!!

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@victorhqc victorhqc commented Mar 1, 2017

Just what I needed :)

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@erasmo-marin erasmo-marin commented Mar 24, 2017

this is great!! I'm using it to animate the scroll. If you want to use some ES6 - ES7 syntax, the @lindell version looks like this, a lot more like functional languages:

    const easeIn  = p => t => Math.pow(t, p);
    const easeOut = p => t => (1 - Math.abs(Math.pow(t-1, p)));
    const easeInOut = p => t => t<.5 ? easeIn(p)(t*2)/2 : easeOut(p)(t*2 - 1)/2+0.5;

then use it like this:

   //power = 3, t = 0.5
   let t = easeInOut(3)(0.5);
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@XerxesNoble XerxesNoble commented Jun 1, 2017

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@bluzky bluzky commented Sep 30, 2017

your gist is awesome

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@AtlasNCz AtlasNCz commented Dec 3, 2017

Great, Thanks1!1!1!

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@MostafaOmarIbrahim MostafaOmarIbrahim commented Dec 13, 2017

Great work, Thank you 👍 <3

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@yukulele yukulele commented Dec 15, 2017

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@ghost ghost commented Jan 12, 2018

This is awesome! Thanks for this resource!

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@ghost ghost commented Jan 24, 2018

What is (--t)?

@RyanG26

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@RyanG26 RyanG26 commented Jan 26, 2018

-- is the decrement operator. It subtracts by one.

If placed before a number, it first subtracts 1 then returns the new value.

If placed after a number, it first returns the number then subtracts 1.

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@wangyi7099 wangyi7099 commented Mar 15, 2018

good! thanks

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@alinq alinq commented Jun 3, 2018

I made the mouse wheel to scroll on the horizontal on a element with this:
document.getElementById('hrz').addEventListener('wheel',event=>this.scrollLeft+=event.deltaY)
Now how do I use EasingFunctions?

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@ImYellowFish ImYellowFish commented Nov 2, 2018

Really helpful. Thanks!

@Herohtar

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@Herohtar Herohtar commented Nov 9, 2018

Since the intended use is 0 <= t <= 1, isn't Math.abs(Math.pow(t-1, p)) the same as Math.pow(1-t, p)?

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@SteverPalm SteverPalm commented Dec 15, 2018

I keep getting unexpected behavior with these. Could somebody please tell me what I'm doing wrong?
I made a simple example here: https://jsfiddle.net/c2vwa6eb/

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@aadityataparia aadityataparia commented Jan 14, 2019

@SteverPalm it should be elemToMove.style.left = easeOutQuad(t) * animationDistance + 'px'; instead of elemToMove.style.left = easeOutQuad(t) * currentDistance + 'px';

@KilliN-SM

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@KilliN-SM KilliN-SM commented Feb 17, 2019

I'm getting spaguetti here, how do I exactly use these functions? Can anyone provide a simple example?

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@RienNeVaPlus RienNeVaPlus commented Feb 25, 2019

2019 speaking, have a version using export: https://gist.github.com/RienNeVaPlus/768ce89b83d8e778bbb46868fd26901b

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@drone1 drone1 commented May 21, 2019

Bless you child.

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@hinell hinell commented Jun 5, 2019

Bless you God.

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@gre gre commented Jun 6, 2019

what happened

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@juan-cortes juan-cortes commented Jun 6, 2019

such helpful, so wow

@HIHIQY1

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@HIHIQY1 HIHIQY1 commented Jun 10, 2019

I agree, this gist is so helpful!

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@vs1998 vs1998 commented Jul 11, 2019

@KilliN-SM i used it for easing the movement of an Object on a HTML Canvas: Codepen Easing Example. This pen is also still WIP

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@dshung1997 dshung1997 commented Oct 24, 2019

Line 23, easeOutQuart: function (t) { return 1-(--t)*t*t*t },. Could somebody tell me what's the meaning of -- ?
If it is the Decrement --, why is it there?

@chriskirknielsen

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@chriskirknielsen chriskirknielsen commented Nov 1, 2019

Line 23, easeOutQuart: function (t) { return 1-(--t)*t*t*t },. Could somebody tell me what's the meaning of -- ?
If it is the Decrement --, why is it there?

@dshung1997 The decrement operation mutates the value of t so that the three following references to t are affected as well.
You could write is as return 1 - (t-1) * (t-1) * (t-1) * (t-1) and get the same result, but as you can see it's a bit more verbose.

You can test this with a little code sample:

var shortFn = (t) => (1-(--t)*t*t*t);
var longFn = (t) => (1 - (t-1) * (t-1) * (t-1) * (t-1));

for (var i = 0; i < 10; i++) {
  var num = Math.floor(Math.random() * 100) / 100;
  console.log(shortFn(num) == longFn(num));
}

Hope this makes more sense for you, now.

@denipriyanto

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@denipriyanto denipriyanto commented Nov 3, 2019

Hello friend ? how can i get the easing of value process from star and end of easing ?

@frollibas

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@frollibas frollibas commented Nov 14, 2019

This is awesome!
Can we get easeInOutExpo in the same way?

@Rkokie

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@Rkokie Rkokie commented Dec 4, 2019

I needed a cubic bezier function to recreate https://cubic-bezier.com/ easing, so I found an article about bezier curves on a canvas and adjusted the code to be a simple timing method.

private easeCubicBezier(t, p1X, p1Y, p2X, p2Y) {
    return 3 * t * Math.pow(1 - t, 2) * p1X + 3 * t * t * (1 - t) * p2X + t * t * t;
}

p1Y and p2Y are not used but I wanted to reflect the exact parameters the css timing function has.

source: http://www.independent-software.com/determining-coordinates-on-a-html-canvas-bezier-curve.html

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@kulikvlad kulikvlad commented Dec 5, 2019

Hello, colleagues, how can I use these formulas to draw graphics on canvas, who has similar material

@tareqdayya

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@tareqdayya tareqdayya commented Dec 7, 2019

this is awesome man, thanks a bunch

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@zenboss zenboss commented Dec 12, 2019

YOU ARE AWESOME !!!

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@codenamezjames codenamezjames commented Jan 3, 2020

👍🎊🔥💯💣

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@jwdunn1 jwdunn1 commented Jan 4, 2020

Also useful for easing is the minimum jerk motion of the 'smootherStep' function:

easeInOutSmoother: function(t) { var ts = t * t, tc = ts * t; return 6*tc*ts - 15*ts*ts + 10*tc },

Example: https://jsfiddle.net/intrinsica/9ryqet30
CSS approximation: cubic-bezier(.49,0,.51,1)

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@thednp thednp commented Jan 15, 2020

@Rkokie

I needed a cubic bezier function to recreate https://cubic-bezier.com/ easing, so I found an article about bezier curves on a canvas and adjusted the code to be a simple timing method.

private easeCubicBezier(t, p1X, p1Y, p2X, p2Y) {
    return 3 * t * Math.pow(1 - t, 2) * p1X + 3 * t * t * (1 - t) * p2X + t * t * t;
}

p1Y and p2Y are not used but I wanted to reflect the exact parameters the css timing function has.

source: http://www.independent-software.com/determining-coordinates-on-a-html-canvas-bezier-curve.html

Do you happen to have a bezier curve function that uses all 4 values?

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@thednp thednp commented Jan 15, 2020

@Rkokie I've read the article and came up with a function

function CubicBezier(cp1x, cp1y, cp2x, cp2y) {

  let BesierEasingFunction
  
  return BesierEasingFunction = t => {

    
    let x = 3 * t * Math.pow(1 - t, 2) * cp1x + 3 * t * t * (1 - t) * cp2x,
    y = 3 * t * Math.pow(1 - t, 2) * cp1y + 3 * t * t * (1 - t) * cp2y 
    
    
    return t === 0 || t === 1 ? t : -Math.atan2(x, y) + 0.5*Math.PI;
  }
}

BUT it doesn't do any interpolation, it just throws some values from time to time, was wondering if you have something that works as an easing function.

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@Rkokie Rkokie commented Jan 15, 2020

@thednp
If you check the article I've posted you'll find the "getBezierXY" method which will use all values, it does require start and end coordinates though. For the timing when easing it appeared making use of all these other parameters didn't make any difference.

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@thednp thednp commented Jan 15, 2020

I replaced sx,sy, with 0 and ex,ey with 1 and I get something moving, but they're not correct.

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@Rkokie Rkokie commented Jan 15, 2020

I see you're using the "getBezierAngle" function, which doesn't calculate the position in the bezier curve but the angle the curve is at, at a certain point in the curve.

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@thednp thednp commented Jan 15, 2020

I used the other function as well, I still don't get the animation to complete, it's like half the distance and wrong coordinates.

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@Rkokie Rkokie commented Jan 15, 2020

I'm curious what you're trying to do that isn't fulfilled with the function I posted. Could you whip up an example in codepen or jsfiddle?

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@thednp thednp commented Jan 15, 2020

As you can see, I'm looking for a simple and working easing function for cubic bezier. Something like tween.js could use such.

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@thednp thednp commented Jan 15, 2020

@Rkokie
To tell you the truth I'm trying to fix some problem with @gre 's script, join us here.

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@jwdunn1 jwdunn1 commented Jan 15, 2020

Not sure how well it works, but try this (found in Ocanvas):

cubicBezier: function (x1, y1, x2, y2, time) {

  // Inspired by Don Lancaster's two articles
  // http://www.tinaja.com/glib/cubemath.pdf
  // http://www.tinaja.com/text/bezmath.html

  // Set start and end point
  var x0 = 0,
    y0 = 0,
    x3 = 1,
    y3 = 1,

    // Convert the coordinates to equation space
    A = x3 - 3*x2 + 3*x1 - x0,
    B = 3*x2 - 6*x1 + 3*x0,
    C = 3*x1 - 3*x0,
    D = x0,
    E = y3 - 3*y2 + 3*y1 - y0,
    F = 3*y2 - 6*y1 + 3*y0,
    G = 3*y1 - 3*y0,
    H = y0,

    // Variables for the loop below
    t = time,
    iterations = 5,
    i, slope, x, y;

  // Loop through a few times to get a more accurate time value, according to the Newton-Raphson method
  // http://en.wikipedia.org/wiki/Newton's_method
  for (i = 0; i < iterations; i++) {

    // The curve's x equation for the current time value
    x = A* t*t*t + B*t*t + C*t + D;

    // The slope we want is the inverse of the derivate of x
    slope = 1 / (3*A*t*t + 2*B*t + C);

    // Get the next estimated time value, which will be more accurate than the one before
    t -= (x - time) * slope;
    t = t > 1 ? 1 : (t < 0 ? 0 : t);
  }

  // Find the y value through the curve's y equation, with the now more accurate time value
  y = Math.abs(E*t*t*t + F*t*t + G*t * H);

  return y;
}

The time parameter varies from 0 through 1, returning the corresponding y value.

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@thednp thednp commented Jan 15, 2020

@jwdunn1 nop, but I thank you for the code.

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@jwdunn1 jwdunn1 commented Jan 15, 2020

The UnitBezier function in this CodePen tracks somewhat closely to the CSS cubic-bezier transition timing function: https://codepen.io/jwdunn/pen/VJGzNm

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@thednp thednp commented Jan 16, 2020

@Jdunn1 confirmed, the UnitBezier kicks some punch and it moves pretty fast as well, thank you.

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@thednp thednp commented Jan 16, 2020

@jwdunn1 if you're looking for an ES6 version, here's one.

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@skylerspark skylerspark commented Jan 17, 2020

Tip, you should convert them to arrow expressions, and dont minify, this is 2020, we dont need minification :D

ALSO you seemed to forget the "var" part of the EasingFunctions variable.

var EasingFunctions = {
 // no easing, no acceleration
 linear: t => {
  return t;
 },
 // accelerating from zero velocity
 easeInQuad: t => {
  return t * t;
 },
 // decelerating to zero velocity
 easeOutQuad: t => {
  return t * (2 - t);
 },
 // acceleration until halfway, then deceleration
 easeInOutQuad: t => {
  return t < 0.5 ? 2 * t * t : -1 + (4 - 2 * t) * t;
 },
 // accelerating from zero velocity
 easeInCubic: t => {
  return t * t * t;
 },
 // decelerating to zero velocity
 easeOutCubic: t => {
  return --t * t * t + 1;
 },
 // acceleration until halfway, then deceleration
 easeInOutCubic: t => {
  return t < 0.5 ? 4 * t * t * t : (t - 1) * (2 * t - 2) * (2 * t - 2) + 1;
 },
 // accelerating from zero velocity
 easeInQuart: t => {
  return t * t * t * t;
 },
 // decelerating to zero velocity
 easeOutQuart: t => {
  return 1 - --t * t * t * t;
 },
 // acceleration until halfway, then deceleration
 easeInOutQuart: t => {
  return t < 0.5 ? 8 * t * t * t * t : 1 - 8 * --t * t * t * t;
 },
 // accelerating from zero velocity
 easeInQuint: t => {
  return t * t * t * t * t;
 },
 // decelerating to zero velocity
 easeOutQuint: t => {
  return 1 + --t * t * t * t * t;
 },
 // acceleration until halfway, then deceleration
 easeInOutQuint: t => {
  return t < 0.5 ? 16 * t * t * t * t * t : 1 + 16 * --t * t * t * t * t;
 }
};
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@gre gre commented Jan 17, 2020

@skylerspark done! it's a snippet, up to you to var it or const it or module.exports= it or export default it ;)

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@mhaidarh mhaidarh commented Feb 23, 2020

@gre Very useful! Thank you very much, Gaëtan!

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@littlefinger1 littlefinger1 commented Jun 9, 2020

Very helpful!

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@temm1210 temm1210 commented Jul 29, 2020

really awesome and useful!! Thank you!!

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