Physically Based Modeling Overview JeongMo Hong Department of

Physically Based Modeling -Overview. Jeong-Mo Hong Department of Computer Science Korea University http: //kucg. korea. ac. kr Graphics Lab @ Korea University

Contents n n n KUCG Introduction Numerical Analysis Rigid Body Cloth Simulation Fluid Control http: //kucg. korea. ac. kr Graphics Lab @ Korea University

Modeling n KUCG What is a model? A model is an idealized and simplified representation of reality n Not always! n http: //kucg. korea. ac. kr Graphics Lab @ Korea University

Motivation n KUCG Can you design the movements and the reactions of 1000 rings? Guendelman et al. 2003 http: //kucg. korea. ac. kr Graphics Lab @ Korea University

Physically Based Animation n Problem definition n How to map a natural phenomena to a computer simulation program? o Mathematical modeling o o o The description of natural phenomena by mathematical equations Differential equations that govern dynamics and geometric representation of objects Numerical simulation o n KUCG Computing an efficient and accurate solution of the mathematical equations Applications n All the phenomena in this world! http: //kucg. korea. ac. kr Graphics Lab @ Korea University

Numerical Analysis - Introduction - http: //kucg. korea. ac. kr Graphics Lab @ Korea University

Rigid Body n KUCG Equations of Motion Guendelman et al. 2003 http: //kucg. korea. ac. kr Graphics Lab @ Korea University

If you want more … n KUCG Topics Collision detection and response n Friction n http: //kucg. korea. ac. kr Graphics Lab @ Korea University

Cloth n KUCG Equations of motion http: //kucg. korea. ac. kr Graphics Lab @ Korea University

If you want more, … n KUCG Topics Collision detection n Sensitivity n Robustness n http: //kucg. korea. ac. kr Graphics Lab @ Korea University

References n Cloth and Rigid body n Physically Based Modeling o o n Real-Time Fluid Dynamics for Games o o Jos Stam Proceedings of the Game Developer Conference, March 2003 Fluid control n Controlling fluid animation with geometric potential o o n David Baraff and Andrew Witkin ACM Siggraph Course Note Fluids n n KUCG Jeong-mo Hong and Chang-Hun Kim Computer Animation and Virtual Worlds, Volume 15, Issue 3 -4, pp. 147 -157, 2004. If you want more, … n Practical Animation of Liquids o o n Visual Simulation of Smoke o o n Foster, N. and Fedkiw, R. SIGGRAPH 2001, 15 -22 (2001) Fedkiw, R. , Stam, J. and Jensen, H. W. SIGGRAPH 2001, 23 -30 (2001) Stable but Responsive Cloth o o Kwang-Jin Choi and Hyeong-Seok Ko. ACM Transactions on Graphics, Vol. 21, Issue 3, pp 604 -611, 2002 http: //kucg. korea. ac. kr Graphics Lab @ Korea University

추가자료 http: //kucg. korea. ac. kr Graphics Lab @ Korea University

A State Vector n State of an object n n KUCG Position and velocity State vector http: //kucg. korea. ac. kr Graphics Lab @ Korea University

Newtonian Mechanics http: //kucg. korea. ac. kr KUCG Graphics Lab @ Korea University

Euler’s Method n Tayler expansion n Euler’s method http: //kucg. korea. ac. kr KUCG Graphics Lab @ Korea University

Stability http: //kucg. korea. ac. kr KUCG Graphics Lab @ Korea University

Implicit Integration http: //kucg. korea. ac. kr KUCG Graphics Lab @ Korea University

Stability http: //kucg. korea. ac. kr KUCG Graphics Lab @ Korea University

KUCG http: //kucg. korea. ac. kr Graphics Lab @ Korea University

Fluid n Equations of motion n Topics KUCG Simulation efficiency n Numerical stability n Object interaction n More and more phenomena n http: //kucg. korea. ac. kr Graphics Lab @ Korea University