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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
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