1. Computer Animation
cgvr.korea.ac.kr

2. 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
cgvr.korea.ac.kr

3. Outline Principles of Animation Keyframe Animation Articulated Figures
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.korea.ac.kr

5. Squash and Stretch
Stretch
Squash
cgvr.korea.ac.kr

6. Slow In and Out
cgvr.korea.ac.kr

7. Anticipation
cgvr.korea.ac.kr

8. Computer Animation Animation Pipeline 3D modeling Motion specification
Motion simulation
Shading, lighting, & rendering
Postprocessing
cgvr.korea.ac.kr

9. Outline Principles of Animation Keyframe Animation Articulated Figures
cgvr.korea.ac.kr

10. Keyframe Animation
Define Character Poses at Specific Time Steps Called “Keyframes”
cgvr.korea.ac.kr

11. Keyframe Animation
Interpolate Variables Describing Keyframes to Determine Poses for Character in between
cgvr.korea.ac.kr

12. Inbetweening Linear Interpolation Usually not enough continuity
cgvr.korea.ac.kr

13. Inbetweening
Spline Interpolation
Maybe good enough
cgvr.korea.ac.kr

14. Inbetweening Spline Interpolation Maybe good enough
May not follow physical laws
cgvr.korea.ac.kr

15. Inbetweening Spline Interpolation Maybe good enough
May not follow physical laws
cgvr.korea.ac.kr

16. Inbetweening
Inverse Kinematics or Dynamics
cgvr.korea.ac.kr

17. Outline Principles of Animation Keyframe Animation Articulated Figures
cgvr.korea.ac.kr

18. Articulated Figures
Character Poses Described by Set of Rigid Bodies Connected by “Joints”
Base
Arm
Hand
Scene Graph
cgvr.korea.ac.kr

19. Articulated Figures Well-Suited for Humanoid Characters
cgvr.korea.ac.kr

20. Articulated Figures
Joints Provide Handles for Moving Articulated Figure
cgvr.korea.ac.kr

21. Inbetweening Compute Joint Angles between Keyframes
consider the length constancy
Right
Wrong
cgvr.korea.ac.kr

22. 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
cgvr.korea.ac.kr

23. Example: Walk Cycle
Hip Joint Orientation:
cgvr.korea.ac.kr

24. Example: Walk Cycle
Knee Joint Orientation:
cgvr.korea.ac.kr

25. Example: Walk Cycle
Ankle Joint Orientation:
cgvr.korea.ac.kr

26. Challenge of Animation
Temporal Aliasing
Motion blur
cgvr.korea.ac.kr

27. Temporal Ailasing Artifacts due to Limited Temporal Resolution
Strobing
Flickering
cgvr.korea.ac.kr

28. Temporal Ailasing Artifacts due to Limited Temporal Resolution
Strobing
Flickering
cgvr.korea.ac.kr

29. Temporal Ailasing Artifacts due to Limited Temporal Resolution
Strobing
Flickering
cgvr.korea.ac.kr

30. Temporal Ailasing Artifacts due to Limited Temporal Resolution
Strobing
Flickering
cgvr.korea.ac.kr

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

32. Summary Animation Requires ... Modeling Scripting Inbetweening
Lighting, shading
Rendering
Image processing
cgvr.korea.ac.kr

33. Kinematics & Dynamics
cgvr.korea.ac.kr

34. Overview Kinematics Dynamics Consider only motion
Determined by positions, velocities, accelerations
Dynamics
Consider underlying forces
Compute motion from initial conditions and physics
cgvr.korea.ac.kr

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

36. 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))
cgvr.korea.ac.kr

37. Forward Kinematics Joint Motions can be Specified by Spline Curves
X=(x, y)
(0, 0)
cgvr.korea.ac.kr

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

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

41. Inverse Kinematics
End-Effector Postions can be Specified by Spline Curves
X=(x, y)
(0, 0)
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: Q1, Q2, Q3
Two equations: x, y
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.korea.ac.kr

44. 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
cgvr.korea.ac.kr

45. Overview Kinematics Dynamics Consider only motion
Determined by positions, velocities, accelerations
Dynamics
Consider underlying forces
Compute motion from initial conditions and physics
cgvr.korea.ac.kr

46. Dynamics Simulation of Physics Insures Realism of Motion
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.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 t0 to t1
with minimum jet fuel:
cgvr.korea.ac.kr

49. Space Time Constraints
Discretize Time Steps
cgvr.korea.ac.kr

50. Space Time Constraints
Solve with Iterative Optimization Methods
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.korea.ac.kr

52. Space Time Constraints
Adapting Motion
Original Jump
Heavier Base
cgvr.korea.ac.kr

53. Space Time Constraints
Adapting Motion
Hurdle
cgvr.korea.ac.kr

54. Space Time Constraints
Adapting Motion
Ski Jump
cgvr.korea.ac.kr

55. Space Time Constraints
Editing Motion
Original
Adapted
cgvr.korea.ac.kr

56. Space Time Constraints
Morphing Motion
The female character morphs into a smaller character during her spine
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.korea.ac.kr

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

59. Summary Kinematics Dynamics Forward kinematics Inverse 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
cgvr.korea.ac.kr

60. Thanks…
cgvr.korea.ac.kr