1. Precomputing Interactive Dynamic Deformable Scenes Doug L.Jams and Kayvon Fatahailian 报告人：宋超

2. Physically Based Modeling and Interactive Simulation  Approach a. Analysis Method: to get analysis solution of the physics equation b. numerical method : FEA,caculus of differences,etc c. data driven ▪ Challenge: a. the difficulty of getting the analysis solution b. no-linear question widely exiting c. how to acquire the data? d. how to use the data?

3. About data-driven  An important strategy  How to identify and control complex systems  Former works ▪ Nelles 2000----Nural Network ▪ Reissell and Pai 2001 ----ARX models ▪ Atkeson et.al.1997---Locally weighted Learning (Lazy learningl) ▪ D.Jams and K. Fatahalian Impulse response functions (IRFs)

4. Precomputing Interactive Dynamic Deformable Scenes  Contribution ▪ black box offline simulators ▪ Dimensional Model Reduction  Excellence ▪ Robust ▪ Real-time ▪ Handle nonlinear deformation ▪ Illumination ▪ can be synthesized on programmable graphics hardware  Using Scope ▪ particular system ▪ very particular interaction conditions

5. Precomputing Interactive Dynamic Deformable Scenes  Procedure ▪ Fore treatment (including mesh,creating the mechanics model) ▪ Dimensional Model Reduction ▪ Analyze the interaction condition ▪ Pre –calculate and create IBFs ▪ Implement

6. About Fore-treatment and acquire deterministic iteractor  Get geometric mesh  Determine the system DOF  Determine the pre-computing According the interaction based on probability.

7. Dimensional Model Reduction(1)  Deterministic static space model Dynamics: Appearance  State nodes:  Time step edge:  Orbits: a temporal sequence of nodes,connected by time step edge  Discrete phase portrait(P): the collection of all pre-computed orbits

8. Dimensional Model Reduction(2)  Model Reduction Detail N state nodes,v vertices N displacement field that is (each u has 3 vector components)

9. Dimensional Model Reduction(3)  Model Reduction Detail ▲ a small number of vibration modes can be sufficient to approximate observed dynamics. (SVD)  Re-parameterization of the phase portrait the state vector:

10. Dimensional Model Reduction(3)  Reduced state vector coordination  ▲displacement  ▲velocity

11. Precomputation Process  Data-driven modeling complication insufficient data;high-demensional state space; divergence of nearby orbits;self-collisions.etc

12. Impulse Response Function  IRFs Index:  IRFs: 

13. Impulse Response Functions(2)  An important special case :

14. Impulse Palettes  Impulse palette based on IRFs:  Impulsively sampling the phase portrait ▲sample time ▲no redundancy ▲orbits terminate

15. Simulate Implement  Blending Impulse Responses Approximate the IRF at That is

16. Example(1)  Dinosaur on moving car dashboard  Plant in moving pot  Cloth on moving door

17. Example(2)  The pre-computing time

18. Example 

19. Example(3)

20. Thank you!