1. Physically Based Modeling -Overview-
Jeong-Mo Hong
Department of Computer Science
Korea University

2. Contents Introduction Numerical Analysis Rigid Body Cloth Simulation
Fluid Simulation
Fluid Control

3. Modeling What is a model?
A model is an idealized and simplified representation of reality
Not always!

4. Motivation
Can you design the movements and the reactions of 1000 rings?
Guendelman et al. 2003

5. Physically Based Animation
Problem definition
How to map a natural phenomena to a computer simulation program?
Mathematical modeling
The description of natural phenomena by mathematical equations
Differential equations that govern dynamics and geometric representation of objects
Numerical simulation
Computing an efficient and accurate solution of the mathematical equations
Applications
All the phenomena in this world!

6. Numerical Analysis - Introduction -

7. Rigid Body
Equations of Motion
Guendelman et al. 2003

8. If you want more …
Topics
Collision detection and response
Friction

9. Cloth
Equations of motion

10. If you want more, …
Topics
Collision detection
Sensitivity
Robustness

11. References Cloth and Rigid body Fluids Fluid control
Physically Based Modeling
David Baraff and Andrew Witkin
ACM Siggraph Course Note
Fluids
Real-Time Fluid Dynamics for Games
Jos Stam
Proceedings of the Game Developer Conference, March 2003
Fluid control
Controlling fluid animation with geometric potential
Jeong-mo Hong and Chang-Hun Kim
Computer Animation and Virtual Worlds, Volume 15, Issue 3-4, pp , 2004.
If you want more, …
Practical Animation of Liquids
Foster, N. and Fedkiw, R.
SIGGRAPH 2001, (2001)
Visual Simulation of Smoke
Fedkiw, R., Stam, J. and Jensen, H.W.
SIGGRAPH 2001, (2001)
Stable but Responsive Cloth
Kwang-Jin Choi and Hyeong-Seok Ko.
ACM Transactions on Graphics, Vol. 21, Issue 3, pp , 2002

12. 추가자료

13. A State Vector
State of an object
Position and velocity
State vector

14. Newtonian Mechanics

15. Euler’s Method
Tayler expansion
Euler’s method

16. Stability

17. Implicit Integration

18. Stability

20. Fluid Equations of motion Topics Simulation efficiency
Numerical stability
Object interaction
More and more phenomena