How I do I make controls/elements move with inertia?

Question

Modern UI's are starting to give their UI elments nice inertia when moving. Tabs slide in, page transitions, even some listboxes and scroll elments have nice inertia to them (the iphone for example). What is the best algorythm for this? It is more than just gravity as they speed up, and then slow down as they fall into place. I have tried various formulae's for speeding up to a maximum (terminal) velocity and then slowing down but nothing I have tried "feels" right. It always feels a little bit off. Is there a standard for this, or is it just a matter of playing with various numbers until it looks/feels right?

Bicycle

Answer 1

You're talking about two different things here.

One is momentum - giving things residual motion when you release them from a drag. This is simply about remembering the velocity of a thing when the user releases it, then applying that velocity to the object every frame and also reducing the velocity every frame by some amount. How you reduce velocity every frame is what you experiment with to get the feel right.

The other thing is ease-in and ease-out animation. This is about smoothly accelerating/decelerating objects when you move them between two positions, instead of just linearly interpolating. You do this by simply feeding your 'time' value through a sigmoid function before you use it to interpolate an object between two positions. One such function is

smoothstep(t) = 3*t*t - 2*t*t*t    [0 <= t <= 1]

This gives you both ease-in and ease-out behaviour. However, you'll more commonly see only ease-out used in GUIs. That is, objects start moving snappily, then slow to a halt at their final position. To achieve that you just use the right half of the curve, ie.

smoothstep_eo(t) = 2*smoothstep((t+1)/2) - 1

Jampack

smoothstep_eo(t) can be simplified into 1.5t-0.5t^3 – Hammel

Answer 2

Mike F's got it: you apply a time-position function to calculate the position of an object with respect to time (don't muck around with velocity; it's only useful when you're trying to figure out what algorithm you want to use.)

Robert Penner's easing equations and demo are superb; like the jQuery demo, they demonstrate visually what the easing looks like, but they also give you a position time graph to give you an idea of the equation behind it.

Siftings

Answer 3

What you are looking for is interpolation. Roughly speaking, there are functions that vary from 0 to 1 and when scaled and translated create nice looking movement. This is quite often used in Flash and there are tons of examples: (NOTE: in Flash interpolation has picked up the name "tweening" and the most popular type of interpolation is known as "easing".)

Have a look at this to get an intuitive feel for the movement types: SparkTable: Visualize Easing Equations.

When applied to movement, scaling, rotation an other animations these equations can give a sense of momentum, or friction, or bouncing or elasticity. For an example when applied to animation have a look at Robert Penners easing demo. He is the author of the most popular series of animation functions (I believe Adobe's built in ones are based on his). This type of transition works equally as well on alpha's (for fade in).

There is a bit of method to the usage. easeInOut start slow, speeds up and the slows down. easeOut starts fast and slows down (like friction) and easeIn starts slow and speeds up (like momentum). Depending on the feel you want you choose the appropriate one. Then you choose between Sine, Expo, Quad and so on for the strength of the effect. The others are easy to work out by their names (e.g. Bounce bounces, Back goes a little further then comes back like an elastic).

Here is a link to the equations from the popular Tweener library for AS3. You should be able to rewrite these in JavaScript (or any other language) with little to no trouble.

Calabar

Answer 4

It's playing with the numbers.. What feels good is good.

I've tried to develop magic formulas myself for years. In the end the ugly hack always felt best. Just make sure you somehow time your animations properly and don't rely on some kind of redraw/refresh rate. These tend to change based on the OS.

Pentangular

Answer 5

Im no expert on this either, but I beleive they are done with quadratic formulas, that, when given the correct parameters, start fast or slow and dramatically increase or decrease towards the end until a certain point is reached.

Fadge