Computer Animation cgvr.korea.ac.kr

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

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

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

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

Slow In and Out cgvr.korea.ac.kr

Anticipation cgvr.korea.ac.kr

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Kinematics & Dynamics cgvr.korea.ac.kr

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

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

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

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

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

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

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

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

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

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

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

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

Dynamics Simulation of Physics Insures Realism of Motion cgvr.korea.ac.kr

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

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

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

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

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

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

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

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

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

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

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

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

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

Thanks… cgvr.korea.ac.kr