Quasi-Rigid Objects in Contact

1. Quasi-Rigid Objects in Contact Mark Pauly Dinesh Pai Leo GuibasStanford University Rutgers University Stanford University

2. Contacts in Simulation • Bio-medical applications: • surgery simulation • artifical joints, dental implants • Mechanical design: • wear and tear of industrial parts • Physics-based animation: • movies • games

3. Existing Models • Rigid body dynamics • small number of state variables • efficient collision detection • contact sensitivity problem (a stool with hundreds of legs) • Fully deformable (e.g. FEM, mass-spring) • accurate modeling of complex materials (elasticity, plasticity) • too costly for models that hardly deform

4. Quasi-Rigid Objects • Physical model • point force applied to object only leads to small, local deformation • analytical system response model to define displacements due to point force • linear elasticity: Global system response by superposition • forces and displacements evaluated on surface only

5. Quasi-Rigid Objects • Surface model • point cloud representation for modeling consistent, highly dynamic contact surface

6. Physical Model • Boussinesq approximation • infinite elastic half-space Poisson’s ratio force at x displacement at y due to force at x shear modulus

7. Physical Model • Boussinesq approximation • system response function

8. Physical Model • Linear elasticity • superposition total displacement at y

9. Volume Preservation • Condition:

10. Volume Preservation

11. Discretization • Approximate system response at discrete nodes (point samples) shape function force at node j displacement at node i

12. Discretization system response matrix vector of tractions [p1,...,pN]T vector of displacements [u1,...,uN]T matrix coefficient

13. Contact • Collision detection • static bounding volume hierarchies (small deformations) • Contact resolution • compute forces and displacements that resolve contact • Contact surface • find contact surface that is consistent for both models

14. Contact Resolution • Collision detection determines points that potentially experience displacements (active nodes) • find corresponding point for each active node active nodes corresponding nodes

15. Contact Resolution • Separation of active nodes • initial separation • final separation

16. Contact Resolution • Condition for contact resolution: • non-negative separation: si≥ 0 • non-negative force: pi≥ 0

17. Contact Resolution • Linear Complementarity Problem (LCP) • solved using Lemke’s method

18. Contact Surface • Consistent conforming contact surface • Adaptive moving least squares (MLS) approximation requires no re-meshing or zippering

19. Simulation • Treat objects as rigid while in free motion • Integrate contact forces to compute total wrench

20. Example • Model acquisition • laser-range scan • Hierarchy construction • recursive clustering • efficient multi-level computation

21. Example • Simulation

22. Example • Validation Measurement Simulation X2 FootSensor (xSensor Corp.) 37 x 13 sensors, 1.94 sensors/cm2

23. Bio-medical Applications • Simulate friction effects to predict attrition  design of artificial joints

24. Computer Animation • Quasi-rigid body simulation

25. Computer Animation • Explicit representation of contact surface allows accurate simulation of friction effects

26. Computer Animation • Explicit representation of contact surface allows accurate simulation of friction effects

27. Conclusion • Quasi-rigid objects bridge the gap between rigid bodies and fully deformable models • Simple and efficient model for contact resolution • Limitations: • small deformations • linear elasticity • sharp corners

28. Future Work • Coupling with low-resolution FEM model • Acquired system response functions • Incorporate friction into LCP • Application: Contact simulation in knee joint

29. Acknowledgements • NSF grants CARGO-0138456, ITR-0205671, IIS-0308157, EIA-0215887, ARO grant DAAD19-03-1-0331 • Anonymous reviewers