Question: I found this [cool website](http://gamemechanicexplorer.com/#easing-1) for game development and it has a list of easing functions: 

![enter image description here](https://i.stack.imgur.com/Q5VXB.png)

Although the site contains a description of what they're for, it goes over my head. What are easing functions and what are they used for?

Update
------

I found a better example of the functions themselves from [Phaser.io's source code](https://github.com/photonstorm/phaser/blob/master/src/tween/Easing.js). These functions are much simpler than the answers here would suggest. They only take one parameter, `k`. As part of the answer, I'd like to know how to use these.

Answer: 
Easing functions are used for interpolation, typically (but not necessarily) in animation / kinematic motion. Linear interpolation (lerp) is something you may have heard of. Let's say you lerp a smiley face from one corner of the screen to another (much as per your image). This means the smiley will move at a steady velocity from point A to point B. If you were to apply this to movement of a limb, it would look very robotic and unnatural -- the actuators / servos that robots use, perform this way. Obviously, human limbs move in a very different way. And most motion that you will see in nature will have interesting motion curves, rather than the steady, unchanging velocity seen in linear interpolation.

Enter easing. Easing motion means the velocity is *not* constant. What this achieves is to look more realistic. Watch people, watch different animals, watch plants bending in the wind, or even how falling rain changes direction on a gusty day. Watch the velocity of a ball as you throw it up in the air and in comes back down again. Watch the motion of a guitar string as you pluck it. Each of these types of motion has a different curve describing velocity.

I suggest you play with [GreenSock's GSAP online](http://www.greensock.com/jump-start-js/) to get a feel for what the different types of easing curves produce in terms of motion. It's one of those things where it takes time and practice to map a particular named curve to the sort of motion you imagine you want. But once you have grasped the basics, you'll have a lot of fun.

P.S. As I said, easing is not only used for animation. It may be used for sound panning, for effecting skeletal motion at the logical / model level, or anything else you can think of that might need specific smooth variation over time.
An easing function lets you interpolate values from one value to another over a given interval using something called an "easing function". These are functions that are designed to take a value and at any given point in the interval, output the value at a certain point in time.

This can be best explained by taking a look at a code snippet: 

```
// simple linear tweening - no easing, no acceleration

Math.linearTween = function (t, b, c, d) {
    return c*t/d + b;
};

```

> 
> @t is the current time (or position) of the tween. This can be seconds or frames, steps, seconds, ms, whatever – as long as the unit is the same as is used for the total time
> 
> 
> @b is the beginning value of the property.
> 
> 
> @c is the change between the beginning and destination value of the property.
> 
> 
> @d is the total time of the tween.
> 
> 
> 

Thanks, <http://upshots.org/actionscript/jsas-understanding-easing>

This is the definition of a linear easing function. Graphing this over time in terms of 't' we get a mere linear graph. 

**Okay, cool. What can we use them, for?**

Any time you have a start and finish in mind and want to animate them, you can use a "tween" or "easing function". 

For example, here's a GIF I just took of Angry Birds:

![enter image description here](https://i.stack.imgur.com/JAiiD.gif)

Notice the menu sliding out to the point in the screen, but it stops slowly? This is due to an easing function that eases into place. You can see those all over the web. If this was a linear ease, it would be the same throughout.

**Music?**

Sure! If we take the value of our current soundtrack value and interpolate it between that and 0 over a total t of say, 1 second then our volume will slowly fade out over a period of one second.

**Bounding Objects**

There are also functions that allow for bouncing (see: <http://easings.net/#easeOutBounce>) which can produce effects like this on a sprite without any physics systems: 

![enter image description here](https://i.stack.imgur.com/fJhtA.gif)

You can find more information on the web by searching for tweening.