1. Computer Graphics
Chapter 12 Computer Animation

2. LET US ENTER INTO THE MAGICAL WORLD OF ANIMATION

3. Contents INTRODUCTION APPLICATIONS DESIGN OF ANIMATION SEQUENCES
GENERAL COMPUTER ANIMATION FUNCTIONS
RASTER ANIMATIONS
COMPUTER ANIMATION LANGUAGES
KEY FRAME SYSTEMS
MOTION SPECIFICATIONS

4. Computer Animation What is Animation? What is Simulation?
Make objects change over time according to scripted actions
What is Simulation?
Predict how objects change over time according to physical laws

5. Introduction
Computer animation is the process used for generating animated images (moving images) using computer graphics.
 Animators are artists who specialize in the creation of animation.
From Latin animātiō, "the act of bringing to life"; from animō ("to animate" or "give life to") and -ātiō ("the act of").
2D ANIMATION
3D ANIMATION

6. APPLICATIONS
Video games
cartoon
Mobile phones

7. Design Of Animation Sequences
Steps for designing animation sequences.
Storyboard Layout
Object definitions
Key frame specifications
Generation of in-between frames

8. Storyboard Layout

9. Object Definitions

10. Key frame Specifications

11. In-between frames

12. GENERAL COMPUTER ANIMATION FUNCTIONS
Animation software provide basic functions to create animation and process the individual object.
Manipulate data object database.
FUNCTIONS
Motion generation.
Object rendering.
Amorphium
Art of illusion

13. Raster Animations
Real-time animations can be generated using raster operations.

14. ORGANISATION OF A VIDEO COLOUR TABLE1
41H 65
255 1
Monitor
24-bit 65
Pixel
value
Red
Green
Blue

15. Computer Animation Languages
GENERAL PURPOSE LANGUAGES:
C,C++,Pascal, or Lisp(control animation sequences).

16. SPECIALIZED ANIMATION LANGUAGES
Key frame systems
Parameterized systems
Scripting systems

17. Key frame Systems

19. Motion Specifications
Various ways in which motions of objects ca be specified as:
Direct Motion Specification.
Goal-Directed Systems.
Kinematics and Dynamics.

20. Direct Motion Specification

21. Goal Directed System

22. Kinematics and Dynamics
Motion parameters such as position , velocity and acceleration are specified without reference to the forces.
INVERSE KINEMATICS:
Initial and final positions of objects at specified times and from that motion parameters .
DYNAMICS:
The forces that produce the velocities and accelerations are specified(physically based modeling).
It uses laws such as Newton’s laws of motion , Euler or Navier -stokes equations.

23. Outline
Principles of Animation
Keyframe Animation
Articulated Figures

24. Principle of Traditional Animation
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

25. Squash and Stretch
Stretch
Squash

26. Slow In and Out

27. Anticipation

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

29. Outline
Principles of Animation
Keyframe Animation
Articulated Figures

30. Keyframe Animation
Define Character Poses at Specific Time Steps Called “Keyframes”

31. Keyframe Animation
Interpolate Variables Describing Keyframes to Determine Poses for Character in between

32. Inbetweening
Linear Interpolation
Usually not enough continuity

33. Inbetweening
Spline Interpolation
Maybe good enough

34. Inbetweening Spline Interpolation Maybe good enough
May not follow physical laws

35. Inbetweening Spline Interpolation Maybe good enough
May not follow physical laws

36. Inbetweening
Inverse Kinematics or Dynamics

37. Outline
Principles of Animation
Keyframe Animation
Articulated Figures

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

39. Articulated Figures
Well-Suited for Humanoid Characters

40. Articulated Figures
Joints Provide Handles for Moving Articulated Figure

41. Inbetweening Compute Joint Angles between Keyframes Right Wrong
consider the length constancy
Right
Wrong

42. Example: Walk Cycle Articulated Figure: Hip Upper Leg (Hip Rotate)
Knee
Lower Leg (Knee Rotate)
Hip Rotate + Knee Rotate
Lower Leg
Ankle
Foot (Ankle Rotate)
Foot

43. Example: Walk Cycle
Hip Joint Orientation:

44. Example: Walk Cycle
Knee Joint Orientation:

45. Example: Walk Cycle
Ankle Joint Orientation:

46. Challenge of Animation
Temporal Aliasing
Motion blur

47. Temporal Ailasing Artifacts due to Limited Temporal Resolution
Strobing
Flickering

48. Temporal Ailasing Artifacts due to Limited Temporal Resolution
Strobing
Flickering

49. Temporal Ailasing Artifacts due to Limited Temporal Resolution
Strobing
Flickering

50. Temporal Ailasing Artifacts due to Limited Temporal Resolution
Strobing
Flickering

51. Motion Blur Composite Weighted Images of Adjacent Frames
Remove parts of signal under-sampled in time

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

53. Overview Kinematics Dynamics Consider only motion
Determined by positions, velocities, accelerations
Dynamics
Consider underlying forces
Compute motion from initial conditions and physics

54. Example: 2-Link Structure
Two Links Connected by Rotational Joints
“End-Effector”
X=(x, y)
(0, 0)

55. X=(l1cosQ1+ l2cos(Q1+Q2), l1sinQ1+ l2sin(Q1+Q2))
Forward Kinematics
Animator Specifies Joint Angles: Q1 and Q2 Computer Finds Positions of End-Effector: X
X=(x, y)
(0, 0)
X=(l1cosQ1+ l2cos(Q1+Q2), l1sinQ1+ l2sin(Q1+Q2))

56. Forward Kinematics Joint Motions can be Specified by Spline Curves
X=(x, y)
(0, 0)

57. Forward Kinematics
Joint Motions can be Specified by Initial Conditions and Velocities
X=(x, y)
(0, 0)

58. Example: 2-Link Structure
What If Animator Knows Position of “End-Effector”
“End-Effector”
X=(x, y)
(0, 0)

59. Inverse Kinematics
Animator Specifies End-Effector Positions: X Computer
Finds Joint Angles: Q1 and Q2
X=(x, y)
(0, 0)

60. Inverse Kinematics
End-Effector Postions can be Specified by Spline Curves
X=(x, y)
(0, 0)

61. Inverse Kinematics Problem for More Complex Structures
System of equations is usually under-defined
Multiple solutions
X=(x, y)
(0, 0)
Three unknowns: Q1, Q2, Q3
Two equations: x, y

62. Inverse Kinematics Solution for More Complex Structures
Find best solution (e.g., minimize energy in motion)
Non-linear optimization
X=(x, y)
(0, 0)

63. Summary Forward Kinematics Inverse 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

64. Overview Kinematics Dynamics Consider only motion
Determined by positions, velocities, accelerations
Dynamics
Consider underlying forces
Compute motion from initial conditions and physics

65. Dynamics
Simulation of Physics Insures Realism of Motion

66. 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

67. 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 t1
with minimum jet fuel:

68. Space Time Constraints
Discretize Time Steps

69. Space Time Constraints
Solve with Iterative Optimization Methods

70. 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

71. Space Time Constraints
Adapting Motion
Original Jump
Heavier Base

72. Space Time Constraints
Adapting Motion
Hurdle

73. Space Time Constraints
Adapting Motion
Ski Jump

74. Space Time Constraints
Editing Motion
Original
Adapted

75. Space Time Constraints
Morphing Motion
The female character morphs into a smaller character during her spine

76. 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

77. Dynamics Other Physical Simulations Rigid bodies Soft bodies Cloth
Liquids
Gases
etc.
Cloth
Hot Gases
cgvr.korea.ac.kr

78. Summary Kinematics Dynamics 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