1. Mixing deformable and rigid- body mechanics simulation Julien Lenoir Sylvère Fonteneau Alcove Project - INRIA Futurs - LIFL - University of Lille (France) 1/23

2. Outlines Introduction Proposition for articulated bodies A generic framework Results 2/23

3. Introduction Mixing different physical formalism ( Newton, Lagrange,… ) Deformable and rigid-body Propose a dedicate architecture for articulated bodies 3/23

4. Introduction - Objectives A physically based simulation of multiple objects (rigid-bodies and/or deformable bodies) with different physical formalism - Constrained these objects = articulated bodies - propose a generic simulation framework dedicated to articulated bodies. 5/23

5. Previous Works [TR 97 Baraff and Witkin] –Constrained different simulators –Iterative algorithm [Visual Computer 03 Jansson and Vergeest] –One object = set of mass-spring/rigid bodies elements 4/23

6. Outlines Previous works, Objectives Proposition for articulated bodies A generic framework Results 6/23

7. Dynamics simulation One object: –Dynamics simulation => ODE of order 2 q degrees of freedom, f external contribution matrices: M (mass), C (viscosity), K (rigidity) –M.A=B Multiple bodies simulation Independent simulation without constraints 7/23

8. Example of heterogeneous simulation Dynamics spline [Remion99]: Lagrange physical formalism, continuous model Rigid-body : Newton-Euler formalism Mass spring net : Newton formalism, discrete model 13/23

9. A generic framework Example of dynamics bodies 16/23

10. Constrain a dynamic simulation The overall constraints method: –Constraint between objects –Lagrange multipliers => –Baumgarte scheme => L.A=E 1 lagrange multiplier (λ i ) for 1 constraint = 1 condition on a degree of freedom (examples: fixed point, plan) 8/23

11. Constrain a dynamic simulation Resolution: Decomposition of the acceleration A [Remion00]: –tendency A t (computed by each object) –correction A c 9/23 Constant Variable

12. Constrain a dynamic simulation Resolution: matrices update automaton star t L & M - 1.L t Local initializations L.M -1.L t Global initialization InitializationRunning Global (mechanics solver) Local (objects) reso l ready update L & M - 1.L t Update L.M -1.L t no change local changes global change ready 10/23

13. Outlines Previous works, Objectives Proposition for articulated bodies A generic framework Results 11/23

14. A generic framework Model n Rotation ArticulatedBodies ArticulableBody Constraint Model 1 Model 2 … FixedPoint Slide … 12/23

15. A generic framework Example of rigid bodies: –Newton-Euler formalism –6 DOF: position (G), orientation ( ) 14/23

16. A generic framework Example of mass-spring net: –Newton formalism –Discrete modele –3n DOF 15/23

17. A generic framework Constraint example: fixed point between two objects (o 1,o 2 ) P(o1)=P(o2) –Spline: P(spline)=P(s,t)= –Rigid Body: P(rigid body)=(Px,Py,Pz) T –Mass-spring: P(mass-spring)=Pi 17/23

18. A generic framework Constraint insertion example –fixed point between spline and rigid object : P rigid body (M)=P spline (0.5,t) –Baumgarte : 18/23

19. Outlines Previous works, Objectives Proposition for articulated bodies A generic framework Results 19/23

20. Soft rings articulation (3 ms on a Bi-Xeon 2,4 GHz) Results 20/23

21. Rigid-bodies articulation (2 ms) Results 21/23

22. Swing articulation (15 ms) Results 22/23

23. Conclusion Proposition to constrain multiple bodies with different physical formalism Drawback : Baumgarte scheme => constraints not necessarily verified at each simulation step 23/23