Interactive Physically-Based Simulation

1. Interactive Physically-Based Simulation John Keyser Department of Computer Science and Engineering Texas A&M University

2. Motivation and Background

3. First, a Little Background • What do we mean by Physically-based Modeling/Simulation? • Why do we do this? • What is its role in graphics?

4. Physically-Based ModelingPhysically-Based Simulation • Modeling, then simulating processes • Based on physical principles

5. Physically-Based ModelingPhysically-Based Simulation • Modeling, then simulating processes • Based on physical principles • Basic idea: come up with a model describing how the environment works

6. Physically-Based ModelingPhysically-Based Simulation • Modeling, then simulating processes • Based on physical principles • Basic idea: come up with a model describing how the environment works • Give an initial state

7. Physically-Based ModelingPhysically-Based Simulation • Modeling, then simulating processes • Based on physical principles • Basic idea: come up with a model describing how the environment works • Give an initial state • Using those equations/relationships/etc. we simulate the results

8. Physically-Based ModelingPhysically-Based Simulation • Modeling, then simulating processes • Based on physical principles • Basic idea: come up with a model describing how the environment works • Give an initial state • Using those equations/relationships/etc. we simulate the results • The model does not have to be real/complete! • But, we usually assume the physical principles are those governing the phenomenon we are modeling

9. Simulating the Real World • Motivation behind many early computer applications • Solving equations from science/engineering • Physically Based Modeling/Simulation remains a topic of continued study, on its own • Scientific Computing/Computational Science

10. Why is PBM Part of Graphics? • Many parts of graphics aim to replicate/simulate the real world, virtually. • Rendering: light interaction and sensing • Modeling: describing real-world geometry • Animation: behavior • Goal is to create a visually plausible result • Sometimes, but not always, want “correct” result

11. Graphics Applications • Offline • Movies • Some (limited) science/engineering studies • Interactive • Games • Training Simulators • Scripting Control Star Wars Episode III, LucasFilm Halo3: Bungie Studios

12. Simulation in Offline Graphics • We can create very good results! • Witness almost any movie • Still plenty of areas to work on • Some still require a lot of user interaction/tuning • Some methods are unstable • Some “higher order” effects aren’t handled • Capturing real-world behavior • etc.

13. How is Interactive Simulation Different? • Rate of simulation • Orders of magnitude difference from offline • Many offline methods are infeasible • The user can control/adjust what happens • Feedback loop • We want the user to be able to direct the simulation

14. What is Interactive? • Action-response cycle • Frequency needed depends on application • Control: .1 to 1 Hz • Smooth video: > 15 to 60 Hz • Force feedback: ~ 1000 Hz • Real-time: same rate as in real world • Not always necessary, desirable, or achievable

15. What is Control? • Letting the user specify the behavior of the simulation • Many ways to do this • Control can give a range of “realism”

16. Goals of My Work • Improving Interactive Simulation • Developing methods that capture phenomena at interactive rates • Providing user control over simulation behavior • These still affect offline simulation • Good interactive models can still be used offline • Control often applied to offline simulation

17. General Approach

18. Physically Based: Modeling Simulation Method for predicting future state from current • Set of defining equations

19. Improving Performance Modeling Simulation Larger time steps More computing power Parallelism Hybridization Multiresolution methods Level of Detail Alternative Formulations • Ignoring terms/effects • Limiting domain • Proxy objects • Statistical model • Phenomenological Model

20. Six Examples • Burning Objects • Simplified Physical Model, Proxy Objects • Plant Motion • Simulation Level of Detail • Waves • Domain Limitation, Identifying Global Effect • Rigid Bodies • Statistical Simulation • Piled Objects • Phenomenological Model, Simulation Control • Smoke Simulation • Simulation Control Conclusion

21. Wave simulation

22. Interactions of Water and Objects • Want to simulate the behavior of water and the objects interacting with water

23. Wave Simulation • 3D fluid simulations are expensive • However, in most applications, the 3D fluid motion is not needed. • Only the behavior at the surface is important • So, simulate waves, instead • Far simpler equation • 2D instead of 3D

24. Wave Particles • Typical approach: discretize the domain • Solve equations on grid • Instead, represent the form of the solution • Represent the solution using particles • Represent a local solution to the wave equation • Behavior ensures global solution • Only under certain conditions • Simulate independently

25. Wave Particles • Local Solution to Wave Equation Local Deviation Function

26. Wave Particles in 2D

27. Wave Particles • Waveform function • C1 and non-zero in a finite range • Easy to create wave trains • Can approximate shapes with larger wavelengths • Suitable for circular motion

28. Wave Particles • Linear Wavefronts Blending Function

29. Expanding/Contracting Wavefronts

30. Wave Particles • Expanding/Contracting Wavefronts Dispersion Angle Wave Particle Origin

31. Wave Particles • Radial Definition • If the distance between wave particles <ri / 2 • Maximum error on wave crest < 0.1% • Maximum error on wave shape < 3%

32. Wave particle origin 2/3 Dispersion angle Subdividing

33. Wave Particles • Wave particles • Collectively represent wavefronts • DO NOT interact • Move independently • Subdivide independently • Into smaller wave particles • Die when too small

34. Water Waves transverse waves

35. Water Waves transverse waves longitudinal waves

36. Water Waves transverse waves longitudinal waves water waves

37. Water Waves • Gerstner 1802

38. Wave Particles • Circular motion is important for • Realistic wave shapes • Realistic object interaction • Realistic wave superposition

39. Wave Particles • Vertical deviation surface vertices

40. Wave Particles • Vertical deviation

41. Wave Particles • Horizontal deviation

42. Wave Particles • Horizontal deviation