Transcript Human Motion Synthesis (II)

Synthesis of Motion from
Simple Animations
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
Examples
Examples
Examples
Examples
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
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
Model
Model

Input to system



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
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
Four Key Stages

Momentum control



Generate physical constraints
Based on Newtonian laws and
biomechanics
Objective function generation


Construct the objective function
Smooth animation, similar to original, and
balanced
Constraints & Stage Detection

Positional constraints

Parameters of detection

Minimal frames required, Tolerance of
intersections, & constrainable body parts
Constraints & Stage Detection

Positional constraints



Wi: Matrix that transforms point p to world
coordinates
x i = Wi p
At time i + 1, p is transformed to:
Wi+1Wi-1Wip
Define Ti+1 = Wi+1Wi-1
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
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
Constraints & Stage Detection

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
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
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
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
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
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
Momentum Control

Momentum during unconstrained
stages



Gravity only external force
Acts on COM
Angular momentum is zero
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)
Momentum Control

Enforce




C1 continuous
at p1 and p4
p2 < p 1
d1 > d 2
p2 < p 4 < p 3
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
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
Conclusion

Environment constraints


Transition pose constraints


Partition motion into constrained and
unconstrained stages
Defined between motion phases by pose
estimator (or user)
Momentum constraints

Dictate behavior of linear/angular momentum
References

C. Karen Liu, Zoran Popovic.
Synthesis of Dynamic Character
Motion from Simple Animations.
SIGGRAPH 2002.

http://grail.cs.washington.edu/projects/
charanim/