jQuery easing function — variables' comprehension

Question

How does the easing function for jQuery work? Take for example:

easeInQuad = function (x, t, b, c, d) {
    return c*(t/=d)*t + b;
};

How does that work? What does each parameter hold? How would I implement some dumb easing for an animation?

Also how would I attach an easing pattern to jQuery, is loading it into $.easing good enough?

Answer 1

According to the jQuery 1.6.2 source, the meaning of the easing function is as follows. The function is called at various points in time during the animation. At the instants it is called,

• x and t both say what the time is now, relative to the start of the animation. x is expressed as a floating point number in the range [0,1], where 0 is the start and 1 is the end. t is expressed in milliseconds since the start of the animation.
• d is the duration of the animation, as specified in the animate call, in milliseconds.
• b=0 and c=1.

The easing function should return a floating point number in the range [0,1], call it r. jQuery then computes x=start+r*(end-start), where start and end are the start and end values of the property as specified in the call to animate, and it sets the property value to x.

As far as I can see, jQuery doesn't give you direct control over when the animation step function is called, it only lets you say "if I am called at time t, then I should be thus far through the entire animation." Therefore you cannot, for example, ask for your object to be redrawn more frequently at times when it is moving faster. Also, I don't know why other people say b is the start value and c is the change -- that's not what jQuery source code says.

If you wanted to define your own easing function to do the same as easeInQuad, for example,

$.extend(jQuery.easing,{myfunc:function(x,t,b,c,d) { return x*x; }})

$('#marker').animate({left:'800px'},'slow','myfunc');

Answer 2

A concrete example,

Suppose our initial value is 1000 and we want to reach 400 in 3s:

var initialValue = 1000,
    destinationValue = 400,
    amountOfChange = destinationValue - initialValue, // = -600
    duration = 3,
    elapsed;

Let's go from 0s to 3s:

elapsed = 0
$.easing.easeInQuad(null, elapsed, initialValue, amountOfChange, duration)
//> 1000

elapsed = 1
$.easing.easeInQuad(null, elapsed, initialValue, amountOfChange, duration)
//> 933.3333333333334

elapsed = 2
$.easing.easeInQuad(null, elapsed, initialValue, amountOfChange, duration)
//> 733.3333333333334

elapsed = 3
$.easing.easeInQuad(null, elapsed, initialValue, amountOfChange, duration)
//> 400

So compared to the synopsis:

$.easing.easeInQuad = function (x, t, b, c, d) {...}

we can deduce:

 x       t          b              c            d
 |       |          |              |            |
null  elapsed  initialValue  amountOfChange  duration

---

NB1: One important thing is that elapsed(t) and duration(d) should be expressed in the same unit, eg: here 'seconds' for us, but could be 'ms' or whatever. This is also true for initialValue(b) and amountOfChange(c), so to sum-up:

 x       t          b              c            d
 |       |          |              |            |
null  elapsed  initialValue  amountOfChange  duration
         ^          ^              ^            ^
         +----------|----=unit=----|------------+
                    +----=unit=----+

NB2: Like @DamonJW, I don't know why x is here. It does not appear in Penner's equations and does not seem to be used in result: let always set him to null

Answer 3

t: current time, b: start value, c: change from the start value to the end value, d: duration.

Here is how it works: http://james.padolsey.com/demos/jquery/easing/ (curve representing when a CSS property is changed).

Here is how I would implement some dumb easing: http://www.timotheegroleau.com/Flash/experiments/easing_function_generator.htm (math is not my strong suit)

You would extend like any of these: http://code.google.com/p/vanitytools/source/browse/trunk/website/js/custom_easing.js?spec=svn29&r=29 - good enough!

Answer 4

This plugin implements the most common easing functions: http://gsgd.co.uk/sandbox/jquery/easing/

Answer 5

Looked through the 1.11 jquery code. The x parameter seems to mean 'percent', independent from initial time value. So, x is always (0 <= x <= 1) (means abstract coefficient), and t is x * d (means time elapsed).