Animation

GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
1
Computer Animation
고려대학교 컴퓨터 그래픽스 연구실
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
2
Computer Animation
 What is Animation?
 Make objects change over time
according to scripted actions


 What is Simulation?
 Predict how objects change over
time according to physical laws


CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
3
Outline
 Principles of Animation
 Keyframe Animation
 Articulated Figures

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
4
Principle of Traditional
Animation – Disney –
 Squash and Stretch
 Slow In and Out
 Anticipation
 Exaggeration
 Follow Through and Overlapping Action
 Timing
 Staging
 Straight Ahead Action and Pose-to-Pose Action
 Arcs
 Secondary Action
 Appeal
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
5
Squash and Stretch
Squash
Stretch
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
6
Slow In and Out
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
7
Anticipation
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
8
Computer Animation
 Animation Pipeline
 3D modeling
 Motion specification
 Motion simulation
 Shading, lighting, & rendering
 Postprocessing

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
9
Outline
 Principles of Animation
 Keyframe Animation
 Articulated Figures

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
10
Keyframe Animation
 Define Character Poses at Specific Time
Steps Called “Keyframes”

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
11
Keyframe Animation
 Interpolate Variables Describing Keyframes
to Determine Poses for Character in between

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
12
Inbetweening
 Linear Interpolation
 Usually not enough continuity
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
13
Inbetweening
 Spline Interpolation
 Maybe good enough
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
14
Inbetweening
 Spline Interpolation
 Maybe good enough
 May not follow physical laws

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
15
Inbetweening
 Spline Interpolation
 Maybe good enough
 May not follow physical laws

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
16
Inbetweening
 Inverse Kinematics or Dynamics

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
17
Outline
 Principles of Animation
 Keyframe Animation
 Articulated Figures

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
18
Articulated Figures
 Character Poses Described by Set of Rigid
Bodies Connected by “Joints”

Base
Arm
Hand
Scene Graph
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
19
Articulated Figures
 Well-Suited for Humanoid Characters
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
20
Articulated Figures
 Joints Provide Handles for Moving
Articulated Figure

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
21
Inbetweening
 Compute Joint Angles between Keyframes
 consider the length constancy

Right Wrong
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
22
Example: Walk Cycle
 Articulated Figure:

Hip
Knee
Foot
Upper Leg
Ankle
Lower Leg
Hip Rotate
Hip Rotate + Knee Rotate
Upper Leg (Hip Rotate)
Foot (Ankle Rotate)
Lower Leg (Knee Rotate)
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
23
Example: Walk Cycle
 Hip Joint Orientation:

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
24
Example: Walk Cycle
 Knee Joint Orientation:

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
25
Example: Walk Cycle
 Ankle Joint Orientation:

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
26
Challenge of Animation
 Temporal Aliasing
 Motion blur

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
27
Temporal Ailasing
 Artifacts due to Limited Temporal Resolution
 Strobing
 Flickering
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
28
Temporal Ailasing
 Artifacts due to Limited Temporal Resolution
 Strobing
 Flickering

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
29
Temporal Ailasing
 Artifacts due to Limited Temporal Resolution
 Strobing
 Flickering

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
30
Temporal Ailasing
 Artifacts due to Limited Temporal Resolution
 Strobing
 Flickering

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
31
Motion Blur
 Composite Weighted Images of Adjacent
Frames
 Remove parts of signal under-sampled in time

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
32
Summary
 Animation Requires ...
 Modeling
 Scripting
 Inbetweening
 Lighting, shading
 Rendering
 Image processing

GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
33
Kinematics &
Dynamics
고려대학교 컴퓨터 그래픽스 연구실
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
34
Overview
 Kinematics
 Consider only motion
 Determined by positions, velocities, accelerations

 Dynamics
 Consider underlying forces
 Compute motion from initial conditions and physics
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
35
Example: 2-Link Structure
 Two Links Connected by Rotational Joints

“End-Effector”
X=(x, y)
(0, 0)
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
36
Forward Kinematics
 Animator Specifies Joint Angles: O
1
and O
2
 Computer Finds Positions of End-Effector: X

X=(x, y)
(0, 0)
X=(l
1
cosO
1
+ l
2
cos(O
1
+O
2
), l
1
sinO
1
+ l
2
sin(O
1
+O
2
))
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
37
Forward Kinematics
 Joint Motions can be Specified by Spline
Curves

X=(x, y)
(0, 0)
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
38
Forward Kinematics
 Joint Motions can be Specified by Initial
Conditions and Velocities

X=(x, y)
(0, 0) ( ) ( )
1 . 0 2 . 1
250 0 60 0
2 1
2 1
÷ =
O
=
O
° = O ° = O
dt
d
dt
d
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
39
Example: 2-Link Structure
 What If Animator Knows Position of “End-
Effector”

“End-Effector”
X=(x, y)
(0, 0)
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
40
Inverse Kinematics
 Animator Specifies End-Effector Positions: X
 Computer Finds Joint Angles: O
1
and O
2

X=(x, y)
(0, 0)
( ) ( )
( ) ( )x l l y l
y l l x l
l l
l l y x
2 2 1 2 2
2 2 1 2 2
1
2 1
2
2
2
1
2 2
1
2
cos sin
cos sin
2
cos
O + + O
O + + O ÷
= O
|
|
.
|


\
|
÷ ÷ +
= O
÷
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
41
Inverse Kinematics
 End-Effector Postions can be Specified by
Spline Curves

X=(x, y)
(0, 0)
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
42
Inverse Kinematics
 Problem for More Complex Structures
 System of equations is usually under-defined
 Multiple solutions

X=(x, y)
(0, 0)
Three unknowns: O
1
, O
2
,

O
3

Two equations: x, y
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
43
Inverse Kinematics
 Solution for More Complex Structures
 Find best solution (e.g., minimize energy in motion)
 Non-linear optimization

X=(x, y)
(0, 0)
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
44
Summary
 Forward Kinematics
 Specify conditions (joint angles)
 Compute positions of end-effectors

 Inverse Kinematics
 “Goal-directed” motion
 Specify goal positions of end effectors
 Compute conditions required to achieve goals

Inverse kinematics provides easier
specification for many animation tasks,
but it is computationally more difficult
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
45
Overview
 Kinematics
 Consider only motion
 Determined by positions, velocities, accelerations

 Dynamics
 Consider underlying forces
 Compute motion from initial conditions and physics
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
46
Dynamics
 Simulation of Physics Insures Realism of
Motion

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
47
Space Time Constraints
 Animator Specifies Constraints
 What the character’s physical structure is
 e.g., articulated figure
 What the character has to do
 e.g., jump from here to there within time t
 What other physical structures are present
 e.g., floor to push off and land
 How the motion should be performed
 e.g., minimize energy

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
48
Space Time Constraints
 Computer Finds the “Best” Physical Motion
 Satisfying constraints
 Example: Particle with Jet Propulsion
 x(t) is position of particle at time t
 f(t) is force of jet propulsion at time t
 Particle’s equation of motion is:

 Suppose we want to move from a to b within t
0
to t
1
with minimum jet fuel:
0 = ÷ ÷
' '
mg f x m
( ) ( ) ( ) b t x a t x dt t f
t
t
= =
}
1 0
2
and subject to Minimize
1
0
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
49
Space Time Constraints
 Discretize Time Steps
b x a x f h
mg f
h
x x x
x m
h
x x x
x
h
x x
x
i
i
i
i i i
i i i
i i
= =
= ÷ ÷
|
.
|

\
|
+ ÷
=
' '
+ ÷
=
' '
÷
=
'
¿
÷ +
÷ +
÷
1 0
2
2
1 1
2
1 1
1
and subject to Minimize
0
2
2
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
50
Space Time Constraints
 Solve with Iterative Optimization Methods

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
51
Space Time Constraints
 Advantages
 Free animator from having to specify details of
physically realistic motion with spline curves
 Easy to vary motions due to new parameters and/or
new constraints

 Challenges
 Specifying constraints and objective functions
 Avoiding local minima during optimization

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
52
Space Time Constraints
 Adapting Motion

Original Jump
Heavier Base
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
53
Space Time Constraints
 Adapting Motion

Hurdle
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
54
Space Time Constraints
 Adapting Motion

Ski Jump
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
55
Space Time Constraints
 Editing Motion

Original Adapted
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
56
Space Time Constraints
 Morphing Motion
The female character morphs into a
smaller character during her spine
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
57
Space Time Constraints
 Advantages
 Free animator from having to specify details of
physically realistic motion with spline curves
 Easy to vary motions due to new parameters and/or
new constraints

 Challenges
 Specifying constraints and objective functions
 Avoiding local minima during optimization

CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
58
Dynamics
 Other Physical Simulations
 Rigid bodies
 Soft bodies
 Cloth
 Liquids
 Gases
 etc.

Cloth
Hot Gases
CGVR
GraphicsLab@KoreaUniversity GraphicsLab@KoreaUniversity
cgvr.korea.ac.kr
59
Summary
 Kinematics
 Forward kinematics
 Animator specifies joints (hard)
 Compute end-effectors (easy)
 Inverse kinematics
 Animator specifies end-effectors (easier)
 Solve for joints (harder)
 Dynamics
 Space-time constraints
 Animator specifies structures & constraints (easiest)
 Solve for motion (hardest)
 Also other physical simulations