Motion Design – Expressions

Expressions

Overview

Expressions are a powerful addition to regular animating with keyframes. They are based on javascript an you can animate layers in a lot of ways by writing a few lines of code.

Once you get over the little “I’m afraid of programming” hurdle expressions will give you so so many opportunities to animate easier and quicker and will improve your workflow immensely.

And you’ll learn some basic Javascript on the way. Win win!!

How to apply

Expressions can be applied to every property you could animate with keyframes.
To quickly add an expression go to the properties stopwatch icon and option + click on it.
You can then directly write your first expression.

gif from motion design school

Expressions = Calculation

Every Expression is a little (or big) calculation that has to have a result at the end. This result is then returned to the property it was applied to.

So for example if you put in the following into the rotation property

100+30

the rotation will be set to 130°.

The expression result must, without any exceptions, be a value that the property can read. Otherwise see the part about Expression errors.

Some properties need one value (rotation, opacity), some two (position, scale,..) and some even three (3D-position,…) or four (color). In these cases we need to use [] to return the the correct values to the property.

[ ]

To output calculation results you can use [ ]. If the property has a single value you do not need it, but if you have more than one value you need to use a so called array:

[value] or value

[value1, value2]
[value1, value2, value3]
[value1, value2, value3, value4]
Example
[200 + 200,10 * 300]

Applied to the position property this will set it to x = 400 and y = 300.

// and ;

If you want to add comments to your code, that only you can read and AE does not you need to add a // in front of it.

Also let’s put a semicolon ; at the end of every line of code. This will tell AE that the line is ended. You don’t necessarily need it at the last line or if there’s only one line of code.

// this is a comment
// you'll need mark every line of comment with these

300 * 2;  // you can also write a comment after a line of code

Variables

In Expressions you can define variables. This makes calculating and reading your code a lot easier.

Example

Let’s try this in the position property:

offset = 300;         // "offset" created and set to 300
x = 200 + offset;     // "x" created, set to 200 and offset added = 500
y = offset;           // "y" created and set to offset = 300
[x,y]                 // x and y returend as final values

The position will be set to 500, 300

Arrays

An array is a collection of one or more values. Its needed for example to deffine the position of an element like [20,10] or the color [0.3,0.4,0.4,0.1].

An array can also be a collection of things like in this example

myfavouritefruit = ["apple", "pear", "berry", "melon"]

Getting one of those values is done by adding [n] after the array name. n being the number of the array element you want to reference starting with 0 for the first one.

myfavouritefruit[0]     // "apple"
myfavouritefruit[1]     // "pear"
myfavouritefruit[2]     // "berry"
myfavouritefruit[3]     // "melon"

In a lot of programming languages counting is startet with 0. Why? Short answer: It makes calculations easier. For longer answers search the web for: “Why computers count from zero”.

Global Variables

These are variables that are defined by AE and that you can use to work with. The most useful ones are value and time

value

Sometimes we want to use the actual value of a property and just add our calculation to it. This is where we need the global variable value After Effects provides for us.

Value represents a number or array of the property at the current time

For single value properties like rotation or opacity writing value will give you that number.

value - 20   // If added to the opacity it will fade the layer 20% 
value + 120   // If add. to the rotation will add 120° to the current rot.

For properties with more than one value that are stored as array, we’ll need to reference which array value we need.

So for example if a layers 3D-position is 300,200,420 and you want to add 20 in every direction you can do this like so:

x = value[0] + 20; // 300 + 20
y = value[1] + 20; // 200 + 20
z = value[2] + 20; // 420 + 20
[x,y,z]

time

The global variable time gives you the value of the current playtime in seconds.

Use this for everything that you want to steadily animate over time.

Example

If you put this in the rotation property it will rotate the element 100° every second.

time * 100

This will rotate the element at half the speed. 360° will be done in 2 second.

time * 360 / 2

Loop Expressions

A Loop is a structure, series, or process, the end of which is connected to the beginning.

You can loop one particular movement or a whole sequence consisting of multiple animations.

In AE you can manually create loops by duplicating keyframes where the last keyframe should always match the first one.

Or you can add expressions to the property you want to loop.

Basic Loop

Repeat keyframes after the last keyframe

loopOut(); 

Repeat keyframes before the first keyframe

loopIn();

Different Kinds of Loops

You can also define the kind of loop.

  • “cycle” – simple repetition of keyframes (default)
  • “pingpong” – back and forth repetition
  • “offset” – adds the value of the keyframes to each repetition as offset
  • “continue” – continues the speed/value of the last keyframe

Here is an example. Notice how you can also add a set repetition amount

loopOut("pingpong",2);

Continuous Loop Trick

If you want to loop all keyframes before and after simply write:

loopIn()+loopOut()-value;

you can combine this with loop kinds as well:

loopIn("pingpong")+loopOut("pingpong")-value; 

Math.sin() and Math.cos()

With these two you can create motion that hovers between values.

The formula for letting variable values hover with Math.sin between -1 and 1 is:

Math.sin(time)

This lets the value go from 0 to 1 to -1 to 0 in 2*π seconds (see the graphic above).

To let the value hover in clean seconds we need to multiply time with π. Like so:

Math.sin(time * Math.PI);

This will hover the value between 0 to 1 to 0 in 1 to -1 to 0 every 2 seconds.

Now we can add a multiplier for the frequency and amplitude:

Math.sin(time * Math.PI * frequency) * amplitude; 

Math.sin(time * Math.PI * 0,5); // Half the speed (every 4 sec.)
Math.sin(time * Math.PI * 2); // Speeds up to double speed (Every sec.)
Math.sin(time * Math.PI) * 100; // Hovers between 100 and -100;
Math.sin(time * Math.PI) * 56; // Hovers between 56 and -56;

Also sometimes you might want to add an offset like so:

Math.sin(time * Math.PI * frequency) * amplitude + offset; 
Math.sin(time * Math.PI * 2) * 5 + 100; // Hovers between 105 and 95;
Math.sin(time * Math.PI * 2) * 50 + 50; // Hovers between 0 and 100;
Example

Put this into the opacity property of an element to let it fade over 4 seconds between 100 and 0 opacity:

Math.sin(time * Math.PI * 0.5) * 50 + 50

If you use this in the scale property it will scale back and forth between 50% and 100% every second:

s = Math.sin(time * Math.PI * 2) * 25 + 75;
[s,s]

Conditional statements: if, else, else if

Use the if statement to specify a block of code to be executed if a condition is true.

if (condition) {
  //  block of code to be executed if the condition is true
}

Use the else statement to specify code to be executed if the condition is false.

if (condition) {
  //  block of code to be executed if the condition is true
} else {
 //  block of code to be executed if the condition is false 
}

Use the else if statement to specify a new condition if the first condition is false. You can create as many else if statements as you like.

if (condition1) {
  //  block of code to be executed if the condition is true
} else if (condition2){
 //  block of code to be executed if condition1 is false but condition2 is true 
} else if (condition...){
 //  block of code to be executed if all conditions before are false but condition... is true 
} else {
 //  block of code to be executed if all before conditions are false 
}

How to write comparisons for conditions

Her are some of the most common ways to compare variables in conditions:

a == b  a is equal to b
a != b  a is not b
a > b   a is more than b
a >= b  a is more than or equal to b
a < b   a is less than b  
a <= b  a is less than or equal to b

Find even more infos here on w3schools

Example
if (cats > 10){
  answer = "You have more than 10 cats";
} else if (cats >= 5) {
  answer = "You have between 5 and 10 cats";
} else {
  answer = "You have less than 5 cats";
}

Math.round() – Math.floor() – Math.ceil()

The Math.round() function returns the value of a number rounded to the nearest integer.

Math.round(0.9); //  result: 1
Math.round(134.2); //  result: 134
Math.round(10.5); //  result: 11

The Math.floor() function returns the value of a number rounded down to the nearest integer.
The Math.ceil() function returns the value of a number rounded up to the nearest integer.
Think of floor and ceiling to remember which one you need 🙂

Math.floor(0.9); //  result: 0
Math.ceil(134.2); //  result: 135
Example
wiggle = wiggle(1,200);
t = Math.round(wiggle/100);
t = t * 100;
[t]

The wiggled value first gets divided by its amplitude -> 100.
Then we use Math.round() to round this value either to 1 or 0 and
multiply this again by 100 to get either 0 or 100 as output []

Shorter version:
t = 100*(Math.round(wiggle(1,200)/100));
[t]

wiggle()

If you want to animate things that have a slightly shaky and random movement without thinking about keyframes go use the wiggle function!

The wiggle function can be applied to any property. So besides position, size, etc. also think about effects that may wiggle.

How about a flickering light, camera shakes, …

Example

If aplied to position: wiggles the element two times per second on the x-Axis
Or wiggles width only if aplied to scale.

x = wiggle(2, 100)[0];
y = value[1];
[x,y]

wiggles between a single value of 0 and 100

wiggle = wiggle(2,100);

t = 100*(Math.round((100-wiggle)/100));
[t]

random()

To make things more interesting we often times need some randomness. This can be provided by the random() expression.

random()         //generates a random value between 0 and 1
random(max) //generates a random number between 0 and a maximum value
random(min,max). //random number between min and max value
Example
random(200)       //random number between 0 and 200
random(20,50).    //random number between 20 and 50

You can also randomize arr

Creating randomness in expressions is an essential part of creating procedural results. Here’s a great tutorial to explore the main methods and functions and look at ways to control, clamp, and refine randomness. And, a few ways to use or deploy randomness in properties to get you thinking about the possibilities.

Use an expression to generate values for an effect

Example:

Create an Echo effect and then position the echoed elements on a circle. Put this into the “Echo Time” property

(10 * 360/(effect(“Echo”)(“Number Of Echoes”)+1))/360;

More Expressions

Want more? here we go!

Here are a bunch if fun tutorials that cover a wide array of expressions.