1. Interactive Manipulation of Rigid Body Simulations Presenter : Chia-yuan Hsiung 9455524 Proceedings of SIGGRAPH 2000 Jovan Popovi´c, Steven M. Seitz, Michael Erdmann, Zoran Popovi´cy, Andrew Witkinz Carnegie Mellon University University of Washington Pixar Animation Studios

2. 2 Outline Introduction Problem & Goal Approach Issues Simulation Algorithm Manipulation with … Results Conclusion Critique

3. 3 Introduction - Problem Physical Simulation programs Auto-Animation Generation Intuitive Control Over Results..? What’s Animators Want? Edit Animation Not Physical Parameters

4. 4 Introduction - Goal Free to Manipulate the Entire Motion Grabbing and changing the state of the object Any location on the trajectory. On multiple object At multiple time The floating time

5. 5 Approach - Issue Sufficient Degree of Freedom Interaction with Real Time Presentation Motion Discontinuity

6. 6 Approach – Interactive Manipulation Simulation Function q : generalized state vector The behavior described by a set of equations In Free flight Add Control Vector, u

7. 7 Approach – Interactive Manipulation Simulation Function Integrating (2) Poisson collision model Impulse applied

8. 8 Approach – Interactive Manipulation Simulation Function Abstract Locally linearize

9. 9 Approach – Interactive Manipulation 2-D Particle Example plot the space of all possible trajectories Converge easily

10. 10 Approach – Manipulation with Jacobian The Efficient computation of Decompose Simulation Function

11. 11 Approach – Manipulation with Jacobian Event Function Applying the Chain Rule

12. 12 Approach – Differential Update Minimized objective function Smallest change Smallest deviation Subject to … M : relative scale between parameters d: desire values for physical parameters

13. 13 Approach – Manipulation with Constraints Constraints State constraint Nails down Expression Constraint Differential expression of q Eg. Floating Constraint Particular event

14. 14 Approach – Manipulation with Discontinuities Smooth Components Loss of Physical Feasibility Degradation of Convergence

15. 15 Approach – Manipulation with Discontinuities Physical Feasibility Polygonal approximations Additional control parameters to vary the surface normal Curvature-dependent polygonal approximations

16. 16 Approach – Manipulation with Discontinuities Convergence The path may not exist Discrete search To account physical feasible regions Jump to smooth components In possible distant regions Selecting smooth components that convergence to the Desire Motion Maintain interactivity

17. 17 Approach – Manipulation with Discontinuities Convergence Sampling Large step size cause diverge Samples the control space Centered around Interaction High dimension of control space make search difficult Animator – Guide Relied

18. 18 Result DEMO

19. 19 Conclusion Provide a hybrid system integrates a motion-construction interactive manipulation tool The animator can rapidly design difficult physical animations Jacobian evaluation Assume the collision function is analytically differentiable. In fact, it may be a linear complementarity problem (LCP)

20. 20 Conclusion Interactive manipulation Could be benefit from specialized rigid body simulator. Not possible for all rigid multi-body systems

21. 21 Critique Good Abstract thoughts If Dragging really easy to get desire result? Not appropriate to more complexity situation.

22. 22 Q & A Thank you~