1 Computer Graphics 15-462 Announcements • Assignment 3 is out – due Tuesday November 5 th at midnight • Midterm on Thursday • Midterm grades are posted—beware, they are artificially high because we haven’t had any exams yet. Cutoff was just 90/80/70. • Programming Assignment 3 and Written assignment 3 are graded
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1Computer Graphics 15-462
Announcements
• Assignment 3 is out – due Tuesday November 5th atmidnight
• Midterm on Thursday• Midterm grades are posted—beware, they are artificially
high because we haven’t had any exams yet. Cutoffwas just 90/80/70.
• Programming Assignment 3 and Written assignment 3are graded
Animation--Simulation
Passive SimulationsBehavioral Animations (lightly)DynamicsActive SimulationsControl Systems
randomlysurface of shapevertex of polygonal object
sizecolortransparencyshapelifetime
DeletionUpdate of position/velocity
translationvortex
Rendering style – motion blur, compositing
What control handlesdo we want/need?
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Karl Sims, Particle Dreams
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Behavioral Animation
• Define rules for the way an object behaves and interacts–models respond to their changing environment–programs implement the rules
• Classic example: “boids” (Craig Reynolds)–object’s motion is a simple function of nearby objects
» Stay near neighbors» Don’t run into them» Move in this general direction
–emergent behavior: flocking–really just a particle system(!)
• Lion King wildebeest stampede
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Equations of Motion
tVV
PP
tAVV
gA
∆++=
∆+==
2
''
'
),,( zyxP =g
V
Integration: accuracy improves as step size decreasesbut never a perfect match
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More generally have other forces
• Unary–Gravity f = mg–Viscous drag: f=-kv
• N-ary–Spring: f=ke
• Spatial interaction forces–Collisions with objects in the environment
NNVVV )(2' •−=
V N
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Spring-Mass Systems
Cloth in 2dJello in 3D
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Spring-Mass Systems
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Cloth
Many types of clothVery different propertiesNot a simple elastic surfaceWoven fabrics tend to be very stiffAnisotropic
Breen ‘95
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Cloth
Increased Resolution of Mesh+Possible Shapes+ Smoothness- Simulation time
Breen ‘95
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Modeling for Clothing
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Collisions for Clothing
Potentially VERY expensiveBounding Box Hierarchy
Partition space or objectsAvoid expensive primitive tests
Polygons Primitive Level
IntermediateLevel(s)
Top Level
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Leaves in the Wind…
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Leaves in the Wind…
uniform sink source vortex
Add together to make interesting fields…
N
ttt
nnn
tn
AvF
vAF
FFF
ανα
==
+=
Wejchert&Haumann, ‘91
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Fracture
O'Brien, J. F., Hodgins, J. K., (1999) Graphical Modelingand Animation of Brittle Fracture. The proceedings ofACM SIGGRAPH 99, Los Angeles, California.
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Fracture
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Smoke
Visual Simulation of Smoke, Ronald Fedkiw Jos Stam Henrik Wann JensenSIGGRAPH 2001, Computer Graphics Proceedings
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Explosions
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Explosions
Yngve, G. D., O'Brien, J. F., Hodgins, J. K., 2000,Animating Explosions. The proceedings of ACMSIGGRAPH 2000.
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The Challenges of Passive Simulation
• Accurate for the situation• What pieces of the physics are necessary
for appearance?• How to give the animator control?
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Dynamics, more generally
• Point mass• Spring/mass systems• Linkages of rigid bodies• Other physical phenomena
–Aerodynamics–Fluids–Fracture–Explosions
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Forward and Inverse Dynamics
forces andtorques accelerations
Forward: given forces and torques what is the motion?
Inverse: given prescribed motion what are theforces and torques?
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What can we simulate?
Open loop
JointsRotary (1,2,3d)
Telescoping jointsClosed loop
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Forces/Torques
GravityWindCollisions/contact
sliding
rolling
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System Description
MassCenter of massMoment of inertia: formula for simple objects
zI
xI
yI
2
)3(12
1
2
22
mrI
LrmII
z
yx
=
+==
Calculate from polygonal model(closed) for more complicated shapes
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Commercially Available Simulation CodeLink: mass, moment of inertiaJoints: degrees of freedom
distance from center of mass of links
Code for equations of motionHooks for applying forces, torques
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Control Systems—how do we do something withthese mechanisms ?
Hierarchy of control:•State machines•Control actions•Low-level servos
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State Machines
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Low-level Control
.
)( θθθτ vdp kk −−=
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Control Actions
Passive strategies where possible
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Control Actions
Synergistic use of joints
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Control Actions
Reduce disturbances
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Control Actions
Physical intuition
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Control Actions
Physical intuition
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Zordan, V. B., Hodgins, J. K., Motion capture-driven simulations thathit and react, Symposium on Computer Animation, 2002.
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Secondary Motion:Coupling Passive and Active Simulations
One-way coupled
Partially coupled
Fully coupled
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The Challenges of Active Simulation
• Control laws are hard to design• Automatic design hasn’t worked for complex
systems (yet)
• Need a larger variety of behaviors• Need to be able to handle new characters easily
• Higher-level behaviors• Realtime performance
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Perceptual Hacks
• How good a job do you have to do?–Objects don’t go through walls
• Viewers can be pretty oblivious of things like incorrectbounces
• And we can’t predict exactly how something shouldbreak
This shift of emphasis from accuracy to fast-and-looks-good is what distinguishes physically based CG from“real” engineering.
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Evaluation
• Side-by-side comparisons• Biomech or engineering data• Turing test?
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Announcements
• Assignment 3 is out – due Tuesday November 5th atmidnight
• Midterm on Thursday• Midterm grades are posted—beware, they are artificially
high because we haven’t had any exams yet. Cutoffwas just 90/80/70.
• Programming Assignment 3 and Written Assignment 3are graded