)(
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)()(' txtrr ii
)()()( 0 txrtRtr ii TT
iiiTii tRrrIrrmtRtI )()()()( 0000
Precomputed
av
a
aaaa rvp Solving for j
JtF
M
nj
M
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M
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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