graphics graphics lab @ korea university cgvr.korea.ac.kr 1 computer animation 고려대학교...

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Graphics cgvr.korea.ac.kr 1 Graphics Lab @ Korea University Graphics Lab @ Korea University Computer Animation 고고고고고 고고고 고고고고 고고고

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Graphics

cgvr.korea.ac.kr 1 Graphics Lab @ Korea University Graphics Lab @ Korea University

Computer Animation

고려대학교 컴퓨터 그래픽스 연구실

cgvr.korea.ac.kr 2

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

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.korea.ac.kr 3

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Outline

Principles of Animation

Keyframe Animation

Articulated Figures

cgvr.korea.ac.kr 4

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

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.korea.ac.kr 5

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Squash and Stretch

Squash

Stretch

cgvr.korea.ac.kr 6

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Slow In and Out

cgvr.korea.ac.kr 7

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Anticipation

cgvr.korea.ac.kr 8

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Computer Animation

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

cgvr.korea.ac.kr 9

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Outline

Principles of Animation

Keyframe Animation

Articulated Figures

cgvr.korea.ac.kr 10

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Keyframe Animation

Define Character Poses at Specific Time Steps Called “Keyframes”

cgvr.korea.ac.kr 11

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Keyframe Animation

Interpolate Variables Describing Keyframes to Determine Poses for Character in between

cgvr.korea.ac.kr 12

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Inbetweening

Linear Interpolation Usually not enough continuity

cgvr.korea.ac.kr 13

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Inbetweening

Spline Interpolation Maybe good enough

cgvr.korea.ac.kr 14

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Inbetweening

Spline Interpolation Maybe good enough

May not follow physical laws

cgvr.korea.ac.kr 15

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Inbetweening

Spline Interpolation Maybe good enough

May not follow physical laws

cgvr.korea.ac.kr 16

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Inbetweening

Inverse Kinematics or Dynamics

cgvr.korea.ac.kr 17

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Outline

Principles of Animation

Keyframe Animation

Articulated Figures

cgvr.korea.ac.kr 18

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Articulated Figures

Character Poses Described by Set of Rigid Bodies Connected by “Joints”

Base

Arm

Hand

Scene Graph

cgvr.korea.ac.kr 19

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Articulated Figures

Well-Suited for Humanoid Characters

cgvr.korea.ac.kr 20

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Articulated Figures

Joints Provide Handles for Moving Articulated Figure

cgvr.korea.ac.kr 21

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Inbetweening

Compute Joint Angles between Keyframes consider the length constancy

Right Wrong

cgvr.korea.ac.kr 22

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

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.korea.ac.kr 23

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Example: Walk Cycle

Hip Joint Orientation:

cgvr.korea.ac.kr 24

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Example: Walk Cycle

Knee Joint Orientation:

cgvr.korea.ac.kr 25

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Example: Walk Cycle

Ankle Joint Orientation:

cgvr.korea.ac.kr 26

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Challenge of Animation

Temporal Aliasing Motion blur

cgvr.korea.ac.kr 27

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Temporal Ailasing

Artifacts due to Limited Temporal Resolution Strobing Flickering

cgvr.korea.ac.kr 28

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Temporal Ailasing

Artifacts due to Limited Temporal Resolution Strobing Flickering

cgvr.korea.ac.kr 29

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Temporal Ailasing

Artifacts due to Limited Temporal Resolution Strobing Flickering

cgvr.korea.ac.kr 30

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Temporal Ailasing

Artifacts due to Limited Temporal Resolution Strobing Flickering

cgvr.korea.ac.kr 31

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Motion Blur

Composite Weighted Images of Adjacent Frames Remove parts of signal under-sampled in time

cgvr.korea.ac.kr 32

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Summary

Animation Requires ... Modeling Scripting Inbetweening Lighting, shading Rendering Image processing

Graphics

cgvr.korea.ac.kr 33 Graphics Lab @ Korea University Graphics Lab @ Korea University

Kinematics & Dynamics

고려대학교 컴퓨터 그래픽스 연구실

cgvr.korea.ac.kr 34

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Overview

Kinematics Consider only motion Determined by positions, velocities, accelerations

Dynamics Consider underlying forces Compute motion from initial conditions and physics

cgvr.korea.ac.kr 35

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Example: 2-Link Structure

Two Links Connected by Rotational Joints

“End-Effector”

X=(x, y)

(0, 0)

cgvr.korea.ac.kr 36

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Forward Kinematics

Animator Specifies Joint Angles: 1 and 2

Computer Finds Positions of End-Effector: X

X=(x, y)

(0, 0)

X=(l1cos1l2cos(1), l1sin1l2sin(1))

cgvr.korea.ac.kr 37

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Forward Kinematics

Joint Motions can be Specified by Spline Curves

X=(x, y)

(0, 0)

cgvr.korea.ac.kr 38

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Forward Kinematics

Joint Motions can be Specified by Initial Conditions and Velocities

X=(x, y)

(0, 0)

1.02.1

2500600

21

21

dt

d

dt

d

1.02.1

2500600

21

21

dt

d

dt

d

cgvr.korea.ac.kr 39

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Example: 2-Link Structure

What If Animator Knows Position of “End-Effector”

“End-Effector”

X=(x, y)

(0, 0)

cgvr.korea.ac.kr 40

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Inverse Kinematics

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

X=(x, y)

(0, 0)

xllyl

yllxl

ll

llyx

22122

221221

21

22

21

221

2

cossin

cossin

2cos

cgvr.korea.ac.kr 41

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Inverse Kinematics

End-Effector Postions can be Specified by Spline Curves

X=(x, y)

(0, 0)

cgvr.korea.ac.kr 42

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Inverse Kinematics

Problem for More Complex Structures System of equations is usually under-defined Multiple solutions

X=(x, y)

(0, 0) Three unknowns: 13

Two equations: x, y

cgvr.korea.ac.kr 43

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

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.korea.ac.kr 44

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

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

Inverse kinematics provides easier specification for many animation tasks, but it is computationally

more difficult

cgvr.korea.ac.kr 45

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Overview

Kinematics Consider only motion Determined by positions, velocities, accelerations

Dynamics Consider underlying forces Compute motion from initial conditions and physics

cgvr.korea.ac.kr 46

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Dynamics

Simulation of Physics Insures Realism of Motion

cgvr.korea.ac.kr 47

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

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.korea.ac.kr 48

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

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 t0 to t1with minimum jet fuel:

0 mgfxm

btxatxdttft

t 10

2 and subject to Minimize

1

0

cgvr.korea.ac.kr 49

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Space Time Constraints

Discretize Time Steps

bxaxfh

mgfh

xxxxm

h

xxxx

h

xxx

ii

iiii

iii

ii

10

2

211

211

1

and subject to Minimize

02

2

cgvr.korea.ac.kr 50

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Space Time Constraints

Solve with Iterative Optimization Methods

cgvr.korea.ac.kr 51

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

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.korea.ac.kr 52

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Space Time Constraints

Adapting Motion

Original Jump

Heavier Base

cgvr.korea.ac.kr 53

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Space Time Constraints

Adapting Motion

Hurdle

cgvr.korea.ac.kr 54

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Space Time Constraints

Adapting Motion

Ski Jump

cgvr.korea.ac.kr 55

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Space Time Constraints

Editing Motion

Original Adapted

cgvr.korea.ac.kr 56

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Space Time Constraints

Morphing Motion

The female character morphs into a smaller character during

her spine

cgvr.korea.ac.kr 57

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

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.korea.ac.kr 58

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

Dynamics

Other Physical Simulations Rigid bodies Soft bodies Cloth Liquids Gases etc.

Cloth

Hot Gases

cgvr.korea.ac.kr 59

CGVR

Graphics Lab @ Korea University Graphics Lab @ Korea University

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