Animation

Outline

Key frame animation Hierarchical animation Inverse kinematics

Key-framing

One hour of animation on film (24fps) requires 86,400 frames

If frames are generated one by one this is an enormous task

Key-framing was first used for feature length animation by Walt Disney ‘Master’ animator draw the key positions Less experience animators draw in-between

frames

Key-framing

Because of its intuitive approach (you put things where you want them at a particular time), this approach is still the most widely used in animation (including 3D computer animation)

In computer animation, the computer generates the in-betweens

The process on the computer

Objects can be positioned, scaled, etc. and a key frame specified

The object can then be repositioned, scaled, etc. and a second key frame generated later in the animation sequence

The computer will then generate the in-between fames

Example

Position a 1 unit square cube six units along the x-axis at frame 1 and scale it by 6 along the y-axis - create a key frame

Move the cube to the origin (0,0,0) and return its size to 111 - create a key frame at frame 60

The computer will then generate the 58 in-between frames

The process: interpolation

The computer interpolates the intermediate values from the start and end values

The simplest kind of interpolation is linear interpolation: if you draw a graph of the parameters (e.g. the x coordinate) against time the variation will be in the straight line

But is this enough?

Interpolation (2)

If you have more than two key frames, linear interpolation is likely to yield disjointed motion - how can we solve this?

Recall splines (from the previous modelling discussion): generate smooth curves through a set of given points for generating smooth surfaces

We can use the same maths for generating smooth surfaces

Interpolation (3)

We can use any of the curves used for shape generation for interpolation with different results

Problems can occur with this kind of interpolation when we move key frames when we try and make an object remain

motionless between movements

Moving key frames

• Because the curve remains smooth and continuous, there may be overshoot

Using ‘identical’ key frames

To make an object stay in a position for a length of time it is natural to define the position at a key frame at the start of the period and one at the end

This may (again) lead to overshoot

Overshoot

Overcoming overshoot

To fix these problems, most key frame systems have a method of controlling the way a parameter changes between key frames

These are often called ease controls because they allow you to ‘ease into’ and ‘ease out of’ a position (also ‘slow in’ and ‘slow out’ are used)

Ease interpolations

Time

Parameter

Slow ease out

Ease out

Slow ease in

Ease in

Ease out-in

Parameter curves

Another way of controlling the key-framed motion of objects is to actually edit the parameter curve

This is the curve generated by the in-betweening process

We can move the control points (key frames), add and delete them and adjust the curve between the control points

Parameter curve editing in Maya

This is done with the ‘spline controls’ and can be done in the ‘Graph Editor’

There are different types of behaviour that can be applied through the key frames: spline, linear, clamped, stepped, flat and fixed.

Motion Graphs

Besides offering the tension, continuity and bias control it also allows dragging, deleting and adding key frames

The motion data is separated into ‘channels’: X, Y, Z position, H, P, B angle and X, Y, Z scale

This gives us a useful visual aid to our animation process

Example: bouncing ball…

Hierarchical animation

Why? Because many real objects are by their nature

hierarchical It allows easy relative movement of objects It allows easy movement of groups of objects

How? By modelling the object as a hierarchy and

manipulating the hierarchy components appropriately

Hierarchical animation: an example

Suppose we want to animate the EIMC logo We want the individual letters to ‘tumble’ from

different directions and combine to form the logo We then want the whole logo spin once and move

off to the right

The easiest way to do this is to build a hierarchical model with the individual letters as nodes

Example (continued)

The ‘eimc’ can be built as a text object The letters are then grouped together Now when the group transformed, each

of the letters will also be transformed Each letter can still be moved

independently

Example (continued)

To do the tumbling letters, each letter can be moved and key-framed independently

Once the letters have come together, the group can be key-framed to move the whole logo

Inverse Kinematics

In the previous example, each node (letter) was manipulated separately

This is OK for relatively simple models, but becomes cumbersome for complex models

If you consider a simple human arm, usually you are concerned with the position of the hand more than the rest of the arm

You generally think ‘move my hand there’ rather than ‘rotate the upper arm through A degrees, rotate lower arm through B degrees, rotate wrist through C degrees’

IK continued

The implementation of this is called inverse kinematics

Kinematics is the study of mechanical motion Inverse refers to the fact that you work

backwards from the desired position to work out the positions of the other objects

In the arm example the positions are worked out up the hierarchy from the hand when normally they would be worked out downwards from the shoulder

IK in CA systems Most modern CA systems (including Maya)

support automatic ‘IK’ing Because many of the hierarchies that are IK’ed

resemble chain-like structures they are called IK chains with each node being a link

When the approach is used for human or animal systems, the IK structure is often called a skeleton and the nodes are called bones

The link is called the effector because its ‘effect’ is on the transformations of all the other nodes

IK in CA systems (cont)

Many joints in real systems have limited motion - this can be defined in most CA systems

It is usually possible to combine IK chains into more complex hierarchies (i.e. join together arms, legs, etc. to form a whole body)

IK skeletons and geometry

So far we have just considered the topology of the object not the geometry

For the final animation we need some geometry to be ‘attached’ to each IK node

There are two common ways to do this...

Attaching geometry to nodes

The simplest method is just to attach a geometric shape to each node E.g. cylinders to simulate fingers, etc.

This is simple, but not very effective for realistic modelling Discontinuities will occur at joints when

large rotation angles are used

Attaching geometry to nodes (2) The second option is to cover the skeleton

in one continuous surface and deform this surface when the skeleton is moved

This is called envelope or skeleton deformation

The skeleton acts like a magnet, attracting points on the envelope when the skeleton is moved

This can be very effective in producing realistic shapes, but there is a problem…

Problem with skeleton deformation

There can be unnatural deformations at the joints of the skeleton

Some systems allow you to control the local deformation of the surface around joints to overcome this.

Practical IK

Can use IK goals for objects or bones – goals are the places you want your IK effectors to move to

You can use hierarchies of objects or bones that distort the geometry around them as in skeleton deformation

IK goals

IK goals are objects that the effector will try and move towards

These can be real objects, or more usually objects that won’t appear in the final rendered scene

If the effector cannot reach the object (due to the fact that it is linked to the other parts of the chain) it moves as close to the goal as it can

IK goals (cont)

You can have multiple goals for different effectors in the chain (e.g. the hand and the elbow may have their goals)

You can also ‘lock’ parts of the chain so they do not rotate

You can stop the parts of the chain rotating about particular axis by deselecting these on the mouse action buttons

IK goals (cont)

You can also specify through what angle the link can rotate through by setting this on the item properties panel

The final parameter you can alter is the ‘stiffness’ of the link This specifies how much a given link

will rotate relative to other links in the chain

Summary

Looked at why and how to use simple key-framing

Covered using hierarchy for animation

Introduced IK and bones