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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

Animation--Simulation

Passive SimulationsBehavioral Animations (lightly)DynamicsActive SimulationsControl Systems

COMPUTER GRAPHICS

15-462

10/21/02

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Overview

• Animation techniques–Traditional animation–Keyframing

–Motion Capture–Simulation

–Behavioral

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Dynamic Simulation

• Realistic motion• High-level control• Design of control routines• Physics of passive systems• Control for the animator?

Antz, PDI/Dreamworks

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Passive—no muscles or motors

Active—internal sources of energy

user

graphics

model

numericalintegrator

state

initialconditions Particle systems

LeavesWater sprayClothing

Running humanTrotting dogSwimming fish

user

desiredbehavior

forces andtorques model

numericalintegrator

graphics

state

control

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Dynamics

• Generate motion by specifying mass and force, applyphysical laws (e.g., Newton’s laws)–particles–soft objects–rigid bodies

• Simulates physical phenomena–gravity–momentum (inertia)–collisions–friction–fluid flow (drag, turbulence, ...)–solidity, flexibility, elasticity–fracture

Maya Dynamics

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Particle Systems

CloudsSmokeFireWaterfallsFireworks

Reeves ’83, the Wrath of KhanBatman Returns, using Reynold’s flocking algorithms

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Particle Systems

Creation—number, initial condiionsposition/velocity

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