Lecture #5 Implicit Method Oh-young Song Sejong University

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Presentation transcript:

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

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

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

Stability: Simple example 1D Particle w/ spring

(Explicit) Euler Method

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.

A Stiff Energy Landscape

(Explicit) Euler Method

(Implicit) Euler Method

(Implicit) Euler Method

Geometrical Interpretation

Large System (Explicit)

Large System

(Linearized) Implicit Method

How about 2nd oder sys.?

How about 2nd oder sys.?

How about 2nd oder sys.?

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

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

Next… Fluids

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