# Lecture 11: Introduction to Animation

How do we animate?

Modifying scene parameters as a function of time.

## Scripting

Specifiying the parameters at every frame.

```
define spinningCube()
rotAngle = pi*frameNumber / 50
```

```
define carScript()
carTranslation = 10*(frameNumber / 100)
wheelRotation = pi*frameNumber / 5
```

### Hierarchical Modeling

This is the order you typically apply rotations:

Why?

- Non-uniform scale will mess up rotations
- Translation will mess up everything

In a hierarchical model, generally do T and R, then `push()`

for S, draw, and `pop()`

before continuing on.
Unless your models are positioned with the origin at where you want it to pivot, you typically also need to do a translate after the rotate but before the scale (because translates mess up everything).

Here’s the (simplified) javascript code for the above example.

```
push(); // upper-arm rectangle (red)
rotate(upperArmRotation);
drawAnchor();
push();
translate(100, 0);
drawRect(200, 100); // box
pop();
push(); // lower-arm rectangle (green)
translate(200, 0);
rotate(lowerArmRotation);
drawAnchor();
push();
translate(100, 0);
drawRect(200, 80); // box
pop();
push(); // hand rectangle (blue)
translate(200, 0);
rotate(handRotation);
drawAnchor();
push();
translate(75, 0);
drawRect(150, 60); // box
pop();
pop();
pop();
pop();
```

The boxes we draw are *centered* at the origin, so we need to translate out the width to get the pivots/anchors we want.

## Key-Framing

**Key-framing** means defining specific animation frames and interpolating between them to get frame-by-frame animation poses.
Typically an artist creates the keyframes.

But how do we interpolate the poses? Can we just use linear interpolation?

For poses and and , which goes from 0 for pose 0 and to 1 for pose 1.

- For positions? Absolutely?
- Scales? Yes.
- Rotations? Nope.

## Outline

- Forward Kinematics/Key framing
- Inverse Kinematics
- Motion capture
- Simulation
- Behavioral Animation
- Physically based (Dynamics)

- Key framing
- Interpolation
- Rotations
- Euler angles
- Quaternions

- Splines
- Skinning
- Kinematics
- Inverse kinematics
- Motion capture
- Collision detection
- Spatial data structures

- Principles of animation
- Squash and stretch
- Timing and motion
- Anticipation
- Follow through
- Arcs
- Ease in/out