Interactive Manipulation of Interactive Manipulation of Rigid Body Simulations Rigid Body Simulations

Presenter : Chia-yuan Hsiung 9455524

Proceedings of SIGGRAPH 2000

Jovan Popovi´c, Steven M. Seitz, Michael Erdmann, Zoran Popovi´cy, Andrew WitkinzCarnegie Mellon UniversityUniversity of WashingtonPixar Animation Studios

2

OutlineOutlineIntroduction

• Problem & Goal

Approach• Issues• Simulation Algorithm• Manipulation with …

ResultsConclusionCritique

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Introduction - Introduction - ProblemProblem

Physical Simulation programs• Auto-Animation Generation• Intuitive Control Over Results..?

What’s Animators Want?• Edit Animation Not Physical Parameters

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Introduction - Introduction - GoalGoal

Free to Manipulate the Entire Motion• Grabbing and changing the state of the object• Any location on the trajectory.• On multiple object• At multiple time• The floating time

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Approach - IssueApproach - Issue

Sufficient Degree of FreedomInteraction with Real Time PresentationMotion Discontinuity

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Approach – Approach – Interactive ManipulationInteractive ManipulationSimulation Function

• q : generalized state vector• The behavior described by a set of equations

• In Free flight

(1) )),(,()( tqtFtqdt

d Add Control Vector , u

(2) ).),(,()( utqtFtqdt

d

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Approach – Approach – Interactive ManipulationInteractive ManipulationSimulation Function

• Integrating (2)

• Poisson collision model• Impulse applied

(3)0 .)),(,()()(0t

tdtutqtFuqtq

(4) ).,( uqIqq

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Approach – Approach – Interactive ManipulationInteractive ManipulationSimulation Function

• Abstract

• Locally linearize

(5) ),()( utStq

(6) u.),(

u

utiSqi (7)

' .uuu

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Approach – Approach – Interactive ManipulationInteractive Manipulation2-D Particle Example

• plot the space of all possible trajectories

• Converge easily

RRS 2:

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Approach – Approach – Manipulation with JacobianManipulation with JacobianThe Efficient computation of

Decompose Simulation Function

u

utiS

),(

(11) ).()()(),( uFuCuFutSccf ttt

)((12)

0

)(

0

0

0

.),,()()(

),),(()(

),,()()(

ut

t

cc

t

ut

tt

cc

c

c

dtu

uqtF

u

uq

du

udtuqutF

u

uF

tduqtFuquF (1) )),(,()( tqtFtqdt

d

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Approach – Approach – Manipulation with JacobianManipulation with JacobianEvent Function

Applying the Chain Rule

(13) 0)),(( qutE c

(14) /

)/()/()(

tE

uqqE

du

udtc

u

uqtF

u

tq

dt

d

),,()(

u

F

u

C

u

F

F

C

C

F

u

utSfff

c

c

c

f ttt

t

t

t

tf

)(

),(

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Approach – Approach – Differential Update Differential UpdateMinimized objective function

• Smallest change• Smallest deviation

(15) )(min uduMu TT

u

uu

utS

),(

q 11Subject to

uu

utS n

),(q n

…

M : relative scale between parameters

d: desire values for physical parameters

(6) u.),(

u

utiSqi

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Approach – Approach – Manipulation with ConstraintsManipulation with ConstraintsConstraints

• State constraint• Nails down

• Expression Constraint• Differential expression of q• Eg.

• Floating Constraint• Particular event

))(())(( iBiA tqvtqv

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Approach – Approach – Manipulation with DiscontinuitiesManipulation with Discontinuities

Smooth Components Loss of Physical Feasibility Degradation of Convergence

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Approach – Approach – Manipulation with DiscontinuitiesManipulation with Discontinuities

Physical FeasibilityPolygonal approximations

• Additional control parameters to vary the surface normal

• Curvature-dependent polygonal approximations

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Approach – Approach – Manipulation with DiscontinuitiesManipulation with Discontinuities

Convergence• The path may not exist• Discrete search

• To account physical feasible regions• Jump to smooth components • In possible distant regions

• Selecting smooth components that convergence to the Desire Motion

• Maintain interactivity

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Approach – Approach – Manipulation with DiscontinuitiesManipulation with DiscontinuitiesConvergence

• Sampling• Large step size cause diverge • Samples the control space• Centered around

• Interaction• High dimension of control space make search difficult• Animator – Guide Relied

u

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ResultResult

DEMO

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ConclusionConclusionProvide a hybrid system

• integrates a motion-construction• interactive manipulation tool• The animator can rapidly design difficult physical anim

ations

Jacobian evaluation• Assume the collision function is analytically differentia

ble.• In fact, it may be a linear complementarity problem (L

CP)

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ConclusionConclusion

Interactive manipulation • Could be benefit from specialized rigid body si

mulator.• Not possible for all rigid multi-body systems

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CritiqueCritique

Good Abstract thoughts

If Dragging really easy to get desire result?

Not appropriate to more complexity situation.

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Q & A

Thank you~Thank you~