Computer Graphics Chapter 12Computer Animation LET US ENTER INTO THE MAGICAL WORLD OF ANIMATION Contents INTRODUCTION APPLICATIONS DESIGN OF ANIMATION SEQUENCES
GENERAL COMPUTER ANIMATION FUNCTIONS RASTER ANIMATIONS COMPUTER ANIMATION LANGUAGES KEY FRAME SYSTEMS MOTION SPECIFICATIONS 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 Introduction Computer animation is the process used for generatinganimated images (moving images) using computer graphics. Animatorsare artists who specialize in the creation of animation. FromLatinanimti, "the act of bringing to life"; fromanim("to animate" or "give life to") and-ti("the act of"). 2D ANIMATION 3D ANIMATION APPLICATIONS Video games cartoon Mobile phones Design Of Animation Sequences
Steps for designing animation sequences. Storyboard Layout Object definitions Key frame specifications Generation of in-between frames Storyboard Layout Object Definitions Key frame Specifications In-between frames 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 Raster Animations Real-time animations can be generated using raster operations. ORGANISATION OF A VIDEO COLOUR TABLE
1 41H 65 255 1 Monitor 24-bit 65 Pixel value Red Green Blue Computer Animation Languages
GENERAL PURPOSE LANGUAGES: C,C++,Pascal, or Lisp(control animation sequences). SPECIALIZED ANIMATION LANGUAGES
Key frame systems Parameterized systems Scripting systems Key frame Systems Motion Specifications
Various ways in which motions of objects ca be specified as: Direct Motion Specification. Goal-Directed Systems. Kinematics and Dynamics. Direct Motion Specification Goal Directed System Kinematics and Dynamics
Motion parameters such as position , velocity andacceleration are specified without reference to the forces. INVERSE KINEMATICS: Initial and final positions of objects atspecified 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 Newtons laws of motion , Euler or Navier -stokes equations. Outline Principles of Animation Keyframe Animation Articulated Figures 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 Squash and Stretch Stretch Squash Slow In and Out Anticipation Computer Animation Animation Pipeline 3D modeling Motion specification
Motion simulation Shading, lighting, & rendering Postprocessing Outline Principles of Animation Keyframe Animation Articulated Figures Keyframe Animation Define Character Poses at Specific Time Steps Called Keyframes Keyframe Animation Interpolate Variables Describing Keyframes to Determine Poses for Character in between Inbetweening Linear Interpolation Usually not enough continuity Inbetweening Spline Interpolation Maybe good enough Inbetweening Spline Interpolation Maybe good enough
May not follow physical laws Inbetweening Spline Interpolation Maybe good enough
May not follow physical laws Inbetweening Inverse Kinematics or Dynamics Outline Principles of Animation Keyframe Animation Articulated Figures Articulated Figures Character Poses Described by Set of Rigid Bodies Connected by Joints Base Arm Hand Scene Graph Articulated Figures Well-Suited for Humanoid Characters Articulated Figures Joints Provide Handles for Moving Articulated Figure Inbetweening Compute Joint Angles between Keyframes Right Wrong
consider the length constancy Right Wrong 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 Example: Walk Cycle Hip Joint Orientation: Example: Walk Cycle Knee Joint Orientation: Example: Walk Cycle Ankle Joint Orientation: Challenge of Animation
Temporal Aliasing Motion blur Temporal Ailasing Artifacts due to Limited Temporal Resolution
Strobing Flickering Temporal Ailasing Artifacts due to Limited Temporal Resolution
Strobing Flickering Temporal Ailasing Artifacts due to Limited Temporal Resolution
Strobing Flickering Temporal Ailasing Artifacts due to Limited Temporal Resolution
Strobing Flickering Motion Blur Composite Weighted Images of Adjacent Frames
Remove parts of signal under-sampled in time Summary Animation Requires ... Scripting Inbetweening
Modeling Scripting Inbetweening Lighting, shading Rendering Image processing Overview Kinematics Dynamics Consider only motion
Determined by positions, velocities, accelerations Dynamics Consider underlying forces Compute motion from initial conditions and physics Example: 2-Link Structure
Two Links Connected by Rotational Joints End-Effector X=(x, y) (0, 0) 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)) Forward Kinematics Joint Motions can be Specified by Spline Curves
X=(x, y) (0, 0) Forward Kinematics Joint Motions can be Specified by Initial Conditions and Velocities X=(x, y) (0, 0) Example: 2-Link Structure
What If Animator Knows Position of End-Effector End-Effector X=(x, y) (0, 0) Inverse Kinematics Animator Specifies End-Effector Positions: X Computer Finds Joint Angles: Q1 and Q2 X=(x, y) (0, 0) Inverse Kinematics End-Effector Postions can be Specified by Spline Curves X=(x, y) (0, 0) 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 Inverse Kinematics Solution for More Complex Structures
Find best solution (e.g., minimize energy in motion) Non-linear optimization X=(x, y) (0, 0) 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 Overview Kinematics Dynamics Consider only motion
Determined by positions, velocities, accelerations Dynamics Consider underlying forces Compute motion from initial conditions and physics Dynamics Simulation of Physics Insures Realism of Motion Space Time Constraints
Animator Specifies Constraints What the characters 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 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 Particles equation of motion is: Suppose we want to move from a to b within t0 to t1 with minimum jet fuel: Space Time Constraints
Discretize Time Steps Space Time Constraints
Solve with Iterative Optimization Methods 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 Space Time Constraints
Adapting Motion Original Jump Heavier Base Space Time Constraints
Adapting Motion Hurdle Space Time Constraints
Adapting Motion Ski Jump Space Time Constraints
Editing Motion Original Adapted Space Time Constraints
Morphing Motion The female character morphs into a smaller character during her spine 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 Dynamics Other Physical Simulations Rigid bodies Soft bodies Cloth
Liquids Gases etc. Cloth Hot Gases cgvr.korea.ac.kr 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