13animation

Graphics

Computer Animation

cgvr.korea.ac.kr

1

Graphics Lab @ Korea University

Computer Animation 

What is Animation? 



CGVR

Make objects change over time according to scripted actions

What is Simulation? 

Predict how objects change over time according to physical laws

Graphics Lab @ Korea University

Outline 

Principles of Animation



Keyframe Animation



Articulated Figures

CGVR

Graphics Lab @ Korea University

Principle of Traditional Animation – Disney –           

CGVR

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

Graphics Lab @ Korea University

Squash and Stretch

CGVR

Stretch Squash

Graphics Lab @ Korea University

Slow In and Out

CGVR

Graphics Lab @ Korea University

Anticipation

CGVR

Graphics Lab @ Korea University

Computer Animation 

CGVR

Animation Pipeline     

3D modeling Motion specification Motion simulation Shading, lighting, & rendering Postprocessing

Graphics Lab @ Korea University

Outline 

Principles of Animation



Keyframe Animation



Articulated Figures

CGVR

Graphics Lab @ Korea University

Keyframe Animation 

CGVR

Define Character Poses at Specific Time Steps Called “Keyframes”

Graphics Lab @ Korea University

Keyframe Animation ď Ž

CGVR

Interpolate Variables Describing Keyframes to Determine Poses for Character in between

Graphics Lab @ Korea University

Inbetweening 

CGVR

Linear Interpolation 

Usually not enough continuity

Graphics Lab @ Korea University

Inbetweening 

CGVR

Spline Interpolation 

Maybe good enough

Graphics Lab @ Korea University

Inbetweening 

CGVR

Spline Interpolation 

Maybe good enough 

May not follow physical laws

Graphics Lab @ Korea University

Inbetweening 

CGVR

Spline Interpolation 

Maybe good enough 

May not follow physical laws

Graphics Lab @ Korea University

Inbetweening ď Ž

CGVR

Inverse Kinematics or Dynamics

Graphics Lab @ Korea University

Outline 

Principles of Animation



Keyframe Animation



Articulated Figures

CGVR

Graphics Lab @ Korea University

Articulated Figures 

CGVR

Character Poses Described by Set of Rigid Bodies Connected by “Joints” Base Arm Hand Scene Graph

Graphics Lab @ Korea University

Articulated Figures ď Ž

CGVR

Well-Suited for Humanoid Characters

Graphics Lab @ Korea University

Articulated Figures ď Ž

CGVR

Joints Provide Handles for Moving Articulated Figure

Graphics Lab @ Korea University

Inbetweening 

CGVR

Compute Joint Angles between Keyframes 

consider the length constancy

Right

Wrong Graphics Lab @ Korea University

Example: Walk Cycle ď Ž

CGVR

Articulated Figure: Hip

Upper Leg (Hip Rotate)

Upper Leg

Hip Rotate Knee Lower Leg

Ankle Foot

Lower Leg (Knee Rotate) Hip Rotate + Knee Rotate Foot (Ankle Rotate)

Graphics Lab @ Korea University

Example: Walk Cycle ď Ž

CGVR

Hip Joint Orientation:

Graphics Lab @ Korea University

Example: Walk Cycle ď Ž

CGVR

Knee Joint Orientation:

Graphics Lab @ Korea University

Example: Walk Cycle ď Ž

CGVR

Ankle Joint Orientation:

Graphics Lab @ Korea University

Challenge of Animation 

CGVR

Temporal Aliasing 

Motion blur

Graphics Lab @ Korea University

Temporal Ailasing 

CGVR

Artifacts due to Limited Temporal Resolution  

Strobing Flickering

Graphics Lab @ Korea University

Temporal Ailasing 

CGVR

Artifacts due to Limited Temporal Resolution  

Strobing Flickering

Graphics Lab @ Korea University

Temporal Ailasing 

CGVR

Artifacts due to Limited Temporal Resolution  

Strobing Flickering

Graphics Lab @ Korea University

Temporal Ailasing 

CGVR

Artifacts due to Limited Temporal Resolution  

Strobing Flickering

Graphics Lab @ Korea University

Motion Blur ď Ž

CGVR

Composite Weighted Images of Adjacent Frames ď Ž

Remove parts of signal under-sampled in time

Graphics Lab @ Korea University

Summary 

CGVR

Animation Requires ...      

Modeling Scripting Inbetweening Lighting, shading Rendering Image processing

Graphics Lab @ Korea University

Graphics

Kinematics & Dynamics

cgvr.korea.ac.kr

33

Graphics Lab @ Korea University

Overview 

Kinematics  



CGVR

Consider only motion Determined by positions, velocities, accelerations

Dynamics  

Consider underlying forces Compute motion from initial conditions and physics

Graphics Lab @ Korea University

Example: 2-Link Structure 

CGVR

Two Links Connected by Rotational Joints

“End­Effector” X=(x, y) (0, 0)

Graphics Lab @ Korea University

Forward Kinematics

CGVR



Animator Specifies Joint Angles: Θ 1 and Θ 2



Computer Finds Positions of End-Effector: X

X=(x, y) (0, 0) X=(l1cosΘ1+ l2cos(Θ1+Θ2), l1sinΘ1+ l2sin(Θ1+Θ2)) Graphics Lab @ Korea University

Forward Kinematics ď Ž

CGVR

Joint Motions can be Specified by Spline Curves

X=(x, y) (0, 0)

Graphics Lab @ Korea University

Forward Kinematics 

CGVR

Joint Motions can be Specified by Initial Conditions and Velocities

X=(x, y) (0, 0)

Θ1 ( 0 ) = 60° Θ 2 ( 0 ) = 250° dΘ1 = 1.2 dt

dΘ 2 = −0.1 dt Graphics Lab @ Korea University

Example: 2-Link Structure 

CGVR

What If Animator Knows Position of “EndEffector” “End­Effector” X=(x, y) (0, 0)

Graphics Lab @ Korea University

Inverse Kinematics  

CGVR

Animator Specifies End-Effector Positions: X Computer Finds Joint Angles: Θ 1 and Θ 2

X=(x, y) (0, 0)

 x 2 + y 2 − l12 − l22   Θ 2 = cos  2l1l2   − ( l2 sin Θ 2 ) x + ( l1 + l2 cos Θ 2 ) y Θ1 = ( l2 sin Θ 2 ) y + ( l1 + l2 cos Θ 2 ) x −1

Graphics Lab @ Korea University

Inverse Kinematics ď Ž

CGVR

End-Effector Postions can be Specified by Spline Curves

X=(x, y) (0, 0)

Graphics Lab @ Korea University

Inverse Kinematics 

CGVR

Problem for More Complex Structures  

System of equations is usually under-defined Multiple solutions X=(x, y)

(0, 0)

Three unknowns: Θ1, Θ2, Θ3 Two equations: x, y Graphics Lab @ Korea University

Inverse Kinematics 

CGVR

Solution for More Complex Structures  

Find best solution (e.g., minimize energy in motion) Non-linear optimization X=(x, y)

(0, 0)

Graphics Lab @ Korea University

Summary 

Forward Kinematics  



CGVR

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 Inverse kinematics provides easier specification for many animation tasks, specification for many animation tasks, but it is computationally more difficult but it is computationally more difficult Graphics Lab @ Korea University

Overview 

Kinematics  



CGVR

Consider only motion Determined by positions, velocities, accelerations

Dynamics  

Consider underlying forces Compute motion from initial conditions and physics

Graphics Lab @ Korea University

Dynamics ď Ž

CGVR

Simulation of Physics Insures Realism of Motion

Graphics Lab @ Korea University

Space Time Constraints 

CGVR

Animator Specifies Constraints 

What the character’s physical structure is 



What the character has to do 



e.g., jump from here to there within time t

What other physical structures are present 



e.g., articulated figure

e.g., floor to push off and land

How the motion should be performed 

e.g., minimize energy

Graphics Lab @ Korea University

Space Time Constraints 

Computer Finds the “Best” Physical Motion 



CGVR

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:

mx′′ − f − mg = 0



Suppose we want to move from a to b within t0 to t1 with minimum jet fuel:

Minimize ∫ f ( t ) dt subject to x( t0 ) = a and x( t1 ) = b t1

2

t0

Graphics Lab @ Korea University

Space Time Constraints 

CGVR

Discretize Time Steps xi − xi −1 x′ = h xi +1 − 2 xi + xi −1 ′ ′ x = h2 xi +1 − 2 xi + xi −1   m x′′ =  − f i − mg = 0 2 h   Minimize h∑ f i subject to x0 = a and x1 = b 2

i

Graphics Lab @ Korea University

Space Time Constraints ď Ž

CGVR

Solve with Iterative Optimization Methods

Graphics Lab @ Korea University

Space Time Constraints 

Advantages  



CGVR

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

Graphics Lab @ Korea University

Space Time Constraints 

CGVR

Adapting Motion

Original Jump

Heavier Base Graphics Lab @ Korea University

Space Time Constraints ď Ž

CGVR

Adapting Motion

Hurdle Graphics Lab @ Korea University

Space Time Constraints 

CGVR

Adapting Motion

Ski Jump Graphics Lab @ Korea University

Space Time Constraints ď Ž

CGVR

Editing Motion

Original

Adapted Graphics Lab @ Korea University

Space Time Constraints 

CGVR

Morphing Motion

The female character morphs into a smaller character during her spine

Graphics Lab @ Korea University

Space Time Constraints 

Advantages  



CGVR

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

Graphics Lab @ Korea University

Dynamics 

CGVR

Other Physical Simulations      

Rigid bodies Soft bodies Cloth Liquids Gases etc.

Cloth

Hot Gases Graphics Lab @ Korea University

Summary 

Kinematics 

Forward kinematics  



Animator specifies joints (hard) Compute end-effectors (easy)

Inverse kinematics  



CGVR

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 Graphics Lab @ Korea University