Advanced Computer Graphics (Spring 2013)

CS 283, Lecture 22:

Physical Simulation 2

Ravi Ramamoorthi

http://inst.eecs.berkeley.edu/~cs283/sp13

Most slides courtesy James O’Brien from CS294-13 Fall 2009

Outline

Rigid bodies: basic physics

Simple springs

Stress and Strain

Numerical Discretization Transition from continuous physics model to

something we can actually do on a computer Important topic in numerical analysis and graphics

Modal Analysis Simplified linear system (reduced dimensional)

Finite Element Method

Disjoint elements tile material domain

Derivatives from shape functions

Nodes shared by adjacent elements

Finite Element Method Disjoint elements tile material domain

Derivatives from shape functions

Nodes shared by adjacent elements

FEM Discretization

Tetrahedral Discretization

Element Shape Functions

Material Derivatives

Recall Elasticity

Node Forces (Green Strain)

Corotational Method

Factor out rotation using polar decomposition Cauchy strain without errors due to rotations

Deformable Object

Outline

Rigid bodies: basic physics

Simple springs

Stress and Strain

Numerical Discretization Transition from continuous physics model to

something we can actually do on a computer Important topic in numerical analysis and graphics

Modal Analysis Simplified linear system (reduced dimensional)

Modal Analysis

Deformation

Example

Sound

Sound Example

Modal Decomposition

Linearization

Normalize for Mass

Diagonalize

Modal Decomposition

Individual Modes

Fast Computation

PS 2 Example

Sound Examples