1. By Naga Govindaraju UNC Chapel Hill naga@cs.unc.edu
Partitioned Dynamics By
Naga Govindaraju
UNC Chapel Hill

2. Overview Problem of tackling different simulation domains
Interleaved simulation
Results
- Particle systems with rigid bodies
- Cloth with rigid bodies
Each simulation problem is best attacked using a specialized technique
Many interactions are decided bilaterally. For example, cloth would in general not affect the user’s motion but consider a cloth sack with fruit where the interaction is bilateral.

3. Problems in Combined Simulation
Quadratic software explosion
Availability of simulation code
Time to merge codes is very expensive
“Least-common-denominator” simulator for combined simulation degrades performance.
Each specialized system is highly optimized based on regularities in objects it models.

4. Modular Approach
Each simulator is a black box with a generic interface.
Difficulties in such an interface involve solving for constraint forces.
Goal – compute constraint forces across interacting systems with minimal knowledge of system’s internals
Difficulties involve satisfying the contact and geometric constraints as they require solving for constraint forces.

5. Overview of Approach Exploit force/acceleration relationship
Matrix-multiply (matrix is explicitly not formed at any point of time).
Interleaved simulation to reduce iterations
(only one or more of the systems satisfy constraints)
Rather than involving in complexities of internals of the systems, apply a force, instruct the system to take a time step and see what it does; resulting change in velocity gives the acceleration.

6. Solving Constraint Forces
Handles for each system
Position – x , velocity and acceleration
Position dependent constraints

8. On Multiple Systems

9. Iterative Solution
To get internal unknown handles, approximate acceleration

10. Constraint Repair
Suppose we compute inaccurate , we need to perform repair.
Geometric constraint satisfied but not passivity.

11. Interleaved Simulation
Exploit disparities in masses

12. Figure 1: 0.23 CPU Seconds per frame on a SGI R10000/199 MHz
Results
Figure 1: 0.23 CPU Seconds per frame on a SGI R10000/199 MHz

13. Figure 2: 3.9 CPU Seconds per frame on a SGI R10000/199 MHz.
Cloth is modelled as a 5054 triangle mesh.

14. Figure 3: 1.27 CPU Seconds per frame on a SGI R10000/199 MHz

15. Figure 4: 5.7 CPU Seconds per frame on a SGI R10000/199 MHz

16. References
Partitioned Dynamics by D. Baraff and A. Witkin tech. report CMU-RI-TR-97-33, Robotics Institute, Carnegie Mellon University, 1997.