1. Lecture #5 Implicit Method Oh-young Song Sejong University
Computer Animation
Implicit Method
Lecture #5
Oh-young Song
Sejong University

2. Give me Stability or Give me Death.
Implicit
What’s “Implicit”?
Stability
Stability is everything in CG.
Give me Stability or Give me Death.
– D. Baraff

3. Stability is Everything!
If step size is big, simulation blows up.
Not good.
So, you must make the step size so small that instability is prevented.
It occurs at nearly every simulation.
Solution
Today: using explosion-resistant method
Research: reformulating the problem

4. Stability: Simple example
1D Particle w/ spring

5. (Explicit) Euler Method

6. Stiff Equation Step size is limited by the largest spring constant k.
System that has some big k’s mixed in are called stiff system.

7. A Stiff Energy Landscape

8. (Explicit) Euler Method

9. (Implicit) Euler Method

10. (Implicit) Euler Method

12. Geometrical Interpretation

17. Large System (Explicit)

18. Large System

19. (Linearized) Implicit Method

20. How about 2nd oder sys.?

21. How about 2nd oder sys.?

22. How about 2nd oder sys.?

23. Term Project (~6.9)
Build your virtual world using animation engine for
Keyframe
Particle
Rigid Body
Fluids
Ex) Game
Or, design your own simulator for
Mobile Device
GPU

24. Term Project (~6.9) Reference Fluid Simulation 2D Rigid Simulation
Plasma Pong
2D Rigid Simulation
BOX2D
Crayon Physics
3D Rigid Simulation
Bullet
Horde3D

25. Next…
Fluids