)(

2'iyi

xx

rm

I

)()(' txtrr ii

)()()( 0 txrtRtr ii TT

iiiTii tRrrIrrmtRtI )()()()( 0000

Precomputed

av

a

aaaa rvp Solving for j

JtF

M

nj

M

Jt

M

Ftav

ˆ

M

njvvvv aaa

ˆ

)ˆ(1 njrI aaaaa

aaaa rvp

Equality Constraint

Computing f based on the changeof the acceleration at Pa

Conditions on the constraint force

• Avoid inter-penetrationdistance between two contact points > 0

• Repulsive forces

• Zero values if contact breaks

Rest contact

Separating

Non-penetration

Repulsive

Zero value if contact breaks

Dynamic Simulation Software

• Open Dynamics Engine (ODE)– Open source library for simulating rigid body dyna

mics– Supports joints, collision detection, and friction

• Coriolis—rigid body dynamics engine in Maya

Video

Jovan Popović, Steven M. Seitz, Michael Erdmann, Zoran Popović, Andrew Witkin “Interactive Manipulation of Rigid Body Simulations” SIGGRAPH 2000