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Graphics Graphics Korea University cgvr.korea.ac.kr 1 Computer Animation 고려대학교 컴퓨터 그래픽스 연구실.

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Presentation on theme: "Graphics Graphics Korea University cgvr.korea.ac.kr 1 Computer Animation 고려대학교 컴퓨터 그래픽스 연구실."— Presentation transcript:

1 Graphics Graphics Lab @ Korea University cgvr.korea.ac.kr 1 Computer Animation 고려대학교 컴퓨터 그래픽스 연구실

2 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 2 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

3 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 3 Outline Principles of Animation Keyframe Animation Articulated Figures

4 CGVR Graphics Lab @ Korea University 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

5 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 5 Squash and Stretch Squash Stretch

6 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 6 Slow In and Out

7 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 7 Anticipation

8 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 8 Computer Animation Animation Pipeline 3D modeling Motion specification Motion simulation Shading, lighting, & rendering Postprocessing

9 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 9 Outline Principles of Animation Keyframe Animation Articulated Figures

10 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 10 Keyframe Animation Define Character Poses at Specific Time Steps Called “Keyframes”

11 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 11 Keyframe Animation Interpolate Variables Describing Keyframes to Determine Poses for Character in between

12 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 12 Inbetweening Linear Interpolation Usually not enough continuity

13 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 13 Inbetweening Spline Interpolation Maybe good enough

14 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 14 Inbetweening Spline Interpolation Maybe good enough  May not follow physical laws

15 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 15 Inbetweening Spline Interpolation Maybe good enough  May not follow physical laws

16 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 16 Inbetweening Inverse Kinematics or Dynamics

17 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 17 Outline Principles of Animation Keyframe Animation Articulated Figures

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

19 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 19 Articulated Figures Well-Suited for Humanoid Characters

20 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 20 Articulated Figures Joints Provide Handles for Moving Articulated Figure

21 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 21 Inbetweening Compute Joint Angles between Keyframes consider the length constancy RightWrong

22 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 22 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)

23 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 23 Example: Walk Cycle Hip Joint Orientation:

24 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 24 Example: Walk Cycle Knee Joint Orientation:

25 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 25 Example: Walk Cycle Ankle Joint Orientation:

26 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 26 Challenge of Animation Temporal Aliasing Motion blur

27 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 27 Temporal Ailasing Artifacts due to Limited Temporal Resolution Strobing Flickering

28 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 28 Temporal Ailasing Artifacts due to Limited Temporal Resolution Strobing Flickering

29 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 29 Temporal Ailasing Artifacts due to Limited Temporal Resolution Strobing Flickering

30 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 30 Temporal Ailasing Artifacts due to Limited Temporal Resolution Strobing Flickering

31 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 31 Motion Blur Composite Weighted Images of Adjacent Frames Remove parts of signal under-sampled in time

32 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 32 Summary Animation Requires... Modeling Scripting Inbetweening Lighting, shading Rendering Image processing

33 Graphics Graphics Lab @ Korea University cgvr.korea.ac.kr 33 Kinematics & Dynamics 고려대학교 컴퓨터 그래픽스 연구실

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

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

36 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 36 Forward Kinematics Animator Specifies Joint Angles:  1 and  2 Computer Finds Positions of End-Effector: X X=(x, y) (0, 0) X=(l 1 cos  1  l 2 cos(  1   ), l 1 sin  1  l 2 sin(  1   ))

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

38 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 38 Forward Kinematics Joint Motions can be Specified by Initial Conditions and Velocities X=(x, y) (0, 0)

39 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 39 Example: 2-Link Structure What If Animator Knows Position of “End- Effector” “End-Effector” X=(x, y) (0, 0)

40 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 40 Inverse Kinematics Animator Specifies End-Effector Positions: X Computer Finds Joint Angles:  1 and  2 X=(x, y) (0, 0)

41 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 41 Inverse Kinematics End-Effector Postions can be Specified by Spline Curves X=(x, y) (0, 0)

42 CGVR Graphics Lab @ Korea University 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:  1      3 Two equations: x, y

43 CGVR Graphics Lab @ Korea University 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)

44 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 44 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

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

46 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 46 Dynamics Simulation of Physics Insures Realism of Motion

47 CGVR Graphics Lab @ Korea University 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

48 CGVR Graphics Lab @ Korea University 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 t 0 to t 1 with minimum jet fuel:

49 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 49 Space Time Constraints Discretize Time Steps

50 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 50 Space Time Constraints Solve with Iterative Optimization Methods

51 CGVR Graphics Lab @ Korea University 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

52 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 52 Space Time Constraints Adapting Motion Original Jump Heavier Base

53 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 53 Space Time Constraints Adapting Motion Hurdle

54 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 54 Space Time Constraints Adapting Motion Ski Jump

55 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 55 Space Time Constraints Editing Motion OriginalAdapted

56 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 56 Space Time Constraints Morphing Motion The female character morphs into a smaller character during her spine

57 CGVR Graphics Lab @ Korea University 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

58 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 58 Dynamics Other Physical Simulations Rigid bodies Soft bodies Cloth Liquids Gases etc. Cloth Hot Gases

59 CGVR Graphics Lab @ Korea University cgvr.korea.ac.kr 59 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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