Keyframe Animation. Computer Animation. Outline. Computer Animation. Keyframe Animation. Keyframe Animation

Transcription

1 Computer Animation What is animation? o Make objects change over time according to scripted actions What is simulation? Pixar o Predict how objects change over time according to physical laws Adam Finkelstein & Tim Weyrich Princeton University C0S 426, Spring 2008 University of Illinois 1 Computer Animation 2 Outline! Keyframe animation Adding inverse kinematics Adding dynamics Pixar Angel Plate Define character poses at specific time steps called keyframes Interpolate variables describing keyframes to determine poses for character in-between 5 6

2 Example: 2-Link Structure Two links connected by rotational joints End-Effector l 1 Forward Kinematics Animator specifies joint angles: and Computer finds positions of end-effector: X 7 8 Forward Kinematics Joint motions can be specified by spline curves Example (online) t 9 10 o Linear interpolation - usually not enough continuity o Spline interpolation - maybe good enough Linear interpolation H&B Figure H&B Figure

3 o Cubic spline interpolation - maybe good enough» May not follow physical laws o Cubic spline interpolation - maybe good enough» May not follow physical laws Articulated figure: Hip joint orientation: Knee joint orientation: Ankle joint orientation: 17 18

4 Example: Ice Skating Outline Keyframe animation Adding inverse kinematics Adding dynamics (Mao Chen, Zaijin Guan, Zhiyan Liu, Xiaohu Qie, CS426, Fall98, Princeton University) Angel Plate Example: 2-Link Structure What if animator knows position of end-effector Inverse Kinematics Animator specifies end-effector positions: X Computer finds joint angles: and : End-Effector Inverse Kinematics End-effector postions can be specified by spline curves Inverse Kinematics Problem for more complex structures o System of equations is usually under-defined o Multiple solutions l 3 x! 3 y t Three unknowns:,,! 3 Two equations: x, y 23 24

5 Inverse Kinematics Solution for more complex structures: o Find best solution (e.g., minimize energy in motion) o Non-linear optimization Example: Ball Boy l 3! 3 Ballboy Fujito, Milliron, Ngan, & Sanocki Princeton University More examples: online Outline Keyframe animation Adding inverse kinematics Adding dynamics Pixar Angel Plate Dynamics Simulation of physics insures realism of motion Animator specifies constraints: o What the character!s physical structure is» e.g., articulated figure o What the character has to do (keyframes)» e.g., jump from here to there within time t o What other physical structures are present» e.g., floor to push off and land o How the motion should be performed» e.g., minimize energy 29 30

6 Computer finds the best physical motion satisfying constraints Solve with iterative optimization methods Example: particle with jet propulsion o x(t) is position of particle at time t o f(t) is force of jet propulsion at time t o Particle!s equation of motion is: o Suppose we want to move from a to b within t0 to t1 with minimum jet fuel: Minimize subject to x(t0)=a and x(t1)=b Advantages: Adapting motion: o Free animator from having to specify details of physically realistic motion with spline curves o Easy to vary motions due to new parameters and/or new constraints Original Jump Challenges: o Specifying constraints and objective functions o Avoiding local minima during optimization Heavier Base Adapting motion: Adapting motion: Hurdle Ski Jump 35 36

7 Advantages: o Free animator from having to specify details of physically realistic motion with spline curves o Easy to vary motions due to new parameters and/or new constraints Example: Manipulation of Sims. Challenges: o Specifying constraints and objective functions o Avoiding local minima during optimization Interactive Manipulation of Rigid Body Simulations. Popovic et al Siggraph Popovic Summary Keyframe animation o Poses specified at key times o In-betweening to fill in the rest Incorporating inverse kinematics o Makes keyframes easier to specify Incorporating dynamics o Makes animation easier to adapt 39