Simple Easing Functions in Javascript - see https://github.com/gre/bezier-easing

easing.js

/*
 * 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
}

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

this is awesome man, thanks a bunch

YOU ARE AWESOME !!!

👍🎊🔥💯💣

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)

@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?

@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.

@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.

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

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.

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.

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?

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

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

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.

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

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

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

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

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;
 }
};

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

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

Very helpful!

really awesome and useful!! Thank you!!

Great gist @gre!

I thought it might be helpful to those who wanted to extend the curves to see how that could be done using higher order functions and increasing the power (Thanks to @lindell for the original snippet! This version however removes the unnecessary Math.abs, reuses easeIn for the easeOut function and changes linear to reference easeIn rather than easeInOut to reduce the complexity for each call (although this definitely isn't an exercise in performance))

const easeIn = p => t => Math.pow(t, p)
const easeOut = p => t => 1 - easeIn(p)(1 - t)
const easeInOut = p => t => t < .5 ? easeIn(p)(t * 2) / 2 : easeOut(p)(t * 2 - 1) / 2 + .5
const Easings = {
	linear: easeIn(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)
}

Knowing this, you can re-write @gre's gist like so:

const Easings = {
	linear = t => t,
	easeInQuad = t => Math.pow(t, 2),
	easeOutQuad = t => 1 - Math.pow(1 - t, 2),
	easeInOutQuad = t => t < .5 ? Math.pow(t * 2, 2) / 2 : (1 - Math.pow(1 - (t * 2 - 1), 2)) / 2 + .5,
	easeInCubic = t => Math.pow(t, 3),
	easeOutCubic = t => 1 - Math.pow(1 - t, 3),
	easeInOutCubic = t => t < .5 ? Math.pow(t * 2, 3) / 2 : (1 - Math.pow(1 - (t * 2 - 1), 3)) / 2 + .5,
	easeInQuart = t => Math.pow(t, 4),
	easeOutQuart = t => 1 - Math.pow(1 - t, 4),
	easeInOutQuart = t => t < .5 ? Math.pow(t * 2, 4) / 2 : (1 - Math.pow(1 - (t * 2 - 1), 4)) / 2 + .5,
	easeInQuint = t => Math.pow(t, 5),
	easeOutQuint = t => 1 - Math.pow(1 - t, 5),
	easeInOutQuint = t => t < .5 ? Math.pow(t * 2, 5) / 2 : (1 - Math.pow(1 - (t * 2 - 1), 5)) / 2 + .5
}

Although it is much more verbose, hopefully it's easier to understand for those who don't understand the pre-decrement tricks

Finally you can take the previous example and substitute parts of the equations to reference each other (cleaning it up a little bit)

const linear = t => t
const easeInQuad = t => Math.pow(t, 2)
const easeOutQuad = t => 1 - easeInQuad(1 - t)
const easeInOutQuad = t => t < .5 ? easeInQuad(t * 2) / 2 : easeOutQuad(t * 2 - 1) / 2 + .5
const easeInCubic = t => Math.pow(t, 3)
const easeOutCubic = t => 1 - easeInCubic(1 - t)
const easeInOutCubic = t => t < .5 ? easeInCubic(t * 2) / 2 : easeOutCubic(t * 2 - 1) / 2 + .5
const easeInQuart = t => Math.pow(t, 4)
const easeOutQuart = t => 1 - easeInQuart(1 - t)
const easeInOutQuart = t => t < .5 ? easeInQuart(t * 2) / 2 : easeOutQuart(t * 2 - 1) / 2 + .5
const easeInQuint = t => Math.pow(t, 5)
const easeOutQuint = t => 1 - easeInQuint(1 - t)
const easeInOutQuint = t => t < .5 ? easeInQuint(t * 2) / 2 : easeOutQuint(t * 2 - 1) / 2 + .5

Great thread!

@aarongeorge thanks a lot! this is super useful! specifically, recently I was wondering how to generate it to any pow, I used this to something unrelated to easing but to do "distribution" => https://greweb.me/plots/109 (making my lines reaching more the edges)

@gre glad I could return the favour! Full credit to @lindell for the original Higher Order implementation. I just wanted to break it down and tweak a few things so it benefits more people.

An alternative (works somehow)

eval(function(p,a,c,k,e,d){e=function(c){return c.toString(36)};if(!''.replace(/^/,String)){while(c--){d[c.toString(a)]=k[c]||c.toString(a)}k=[function(e){return d[e]}];e=function(){return'\\w+'};c=1};while(c--){if(k[c]){p=p.replace(new RegExp('\\b'+e(c)+'\\b','g'),k[c])}}return p}('f d={c:3(n){0 n},g:3(n){0 n*n},a:3(n){0 n*(2-n)},7:3(n){0 n<.5?2*n*n:(4-2*n)*n-1},9:3(n){0 n*n*n},b:3(n){0--n*n*n+1},e:3(n){0 n<.5?4*n*n*n:(n-1)*(2*n-2)*(2*n-2)+1},k:3(n){0 n*n*n*n},h:3(n){0 1- --n*n*n*n},i:3(n){0 n<.5?8*n*n*n*n:1-8*--n*n*n*n},l:3(n){0 n*n*n*n*n},j:3(n){0 1+--n*n*n*n*n},m:3(n){0 n<.5?6*n*n*n*n*n:1+6*--n*n*n*n*n}};',24,24,'return|||function|||16|easeInOutQuad||easeInCubic|easeOutQuad|easeOutCubic|linear|EasingFunctions|easeInOutCubic|var|easeInQuad|easeOutQuart|easeInOutQuart|easeOutQuint|easeInQuart|easeInQuint|easeInOutQuint|'.split('|'),0,{}))

visual cheat sheet https://easings.net/