1. Synthesis of Motion from Simple Animations

2. Introduction Produce realistic character motion from simple animation
Non-skilled animator can quickly produce believable animation sequences
System is based on constraints of input motion

3. Examples

4. Examples

5. Examples

6. Examples

7. Realism Character must satisfy laws of physics
Many possible muscle configurations
Small subset appear realistic
Computing correct dynamics  complex math
Tradeoff
Level of control by animator
Artistic freedom vs. physical correctness

8. Process Animator creates rough sketch of desired animation
Small set of essential keyframes
System can make recommendations
System infers environmental constraints
Focus on forces essential to realistic animation
No need to solve for all muscle forces

9. Model

10. Model Input to system Spacetime optimization
Articulated character with mass distribution
Values of joint angles at each frame
Spacetime optimization
Solve for unknowns
Values of joint angles
Angular and linear momentums

11. Four Key Stages Constraint and stage detection
Automatically detect environment constraints
Separate original sequence into constrained and unconstrained stages
Transition pose generation
Establish poses between constrained and unconstrained stages

12. Four Key Stages Momentum control Objective function generation
Generate physical constraints
Based on Newtonian laws and biomechanics
Objective function generation
Construct the objective function
Smooth animation, similar to original, and balanced

13. Constraints & Stage Detection
Positional constraints
Parameters of detection
Minimal frames required, Tolerance of intersections, & constrainable body parts

14. Constraints & Stage Detection
Positional constraints
Wi: Matrix that transforms point p to world coordinates
xi = Wip
At time i + 1, p is transformed to:
Wi+1Wi-1Wip
Define Ti+1 = Wi+1Wi-1

15. Constraints & Stage Detection
Positional constraints
Constraint on point p from time 1 to n implies T1 through Tn all bring p to same global position
Tixi = xi, or (Ti – I)xi = 0
Solution can be either point, line, or plane

16. Constraints & Stage Detection
Sliding constraints
Instead of fixing a point, allow it to slide along a line (or plane)
e.g. foot of a figure skater
Point p constrained to line L:
minp,l ∑ Dist(TiWip,L)
Minimize sum of distances between xi and the line L at each frame

17. Constraints & Stage Detection
Given detected constraints, separate original animation
Unconstrained (flight)
Constrained (ground)
Different physics/biomechanics rules for each
During unconstrained, gravity is the only external force

18. Transition Pose Generation
Transition poses occur at boundaries of stages
Store parameters about transition poses for example motions
Generated by animators
Motion captured data
Update database of motions

19. Transition Pose Generation
Training input parameters (e.g. jump)
Flight distance
Landing angle
Average horizontal speed, etc.
Output is three center of mass points
Lower body
Upper body
Two arms

20. Transition Pose Generation
Predict a candidate pose
K nearest neighbor algorithm
Select at most k similar examples
Compute candidate pose
Three center of mass points
Interpolate poses of selected neighbors
Weighted by similarities to input sequence

21. Transition Pose Generation
Construct full character pose
Inverse kinematics problem
Minimize deviation between suggested and original poses
Advantages to estimating small set of parameters
Joint angles not uniformly scaled
Same motion capture database for different skeletal structures

22. Transition Pose Generation
Transition to different skeletal structure
CA: COM output parameter of character A
ĈA, ĈB: Corresponding COM for default pose
Intuitively, displace COM parameter by rescaled difference between default and suggested pose of character in database

23. Momentum Control Momentum during unconstrained stages
Gravity only external force
Acts on COM
Angular momentum is zero

24. Momentum Control Momentum during constrained stages
No complex physical simulation
Based on biomechanics studies and behavior of motion captured data
Natural dynamic motion
First store energy (momentum decreases)
Energy burst (small overshoot)

25. Momentum Control Enforce C1 continuous at p1 and p4 p2 < p1
d1 > d2
p2 < p4 < p3

26. Objective Function Final check on realism Minimum mass displacement
Compute integral of mass displacement over body
Achieves natural joint movement
Example: bending at waist instead of knees
Minimal velocity of DOFs
For time coherence (smoother)
Effectively minimize velocity of joint angles

27. Objective Function
Static balance
During constrained stages where character is standing still
Analyze COM when projected onto plane normal to gravity
Spacetime objective function is a weighted sum of these

28. Conclusion Environment constraints Transition pose constraints
Partition motion into constrained and unconstrained stages
Transition pose constraints
Defined between motion phases by pose estimator (or user)
Momentum constraints
Dictate behavior of linear/angular momentum

29. References
C. Karen Liu, Zoran Popovic. Synthesis of Dynamic Character Motion from Simple Animations. SIGGRAPH 2002.