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Advanced Computer Graphics (Spring 2013)

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

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Advanced Computer Graphics (Spring 2013)

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  1. 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

  2. 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)

  3. Finite Element Method • Disjoint elements tile material domain • Derivatives from shape functions • Nodes shared by adjacent elements

  4. Finite Element Method • Disjoint elements tile material domain • Derivatives from shape functions • Nodes shared by adjacent elements

  5. FEM Discretization

  6. Tetrahedral Discretization

  7. Element Shape Functions

  8. Material Derivatives

  9. Recall Elasticity

  10. Node Forces (Green Strain)

  11. Corotational Method • Factor out rotation using polar decomposition • Cauchy strain without errors due to rotations

  12. Deformable Object

  13. 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)

  14. Modal Analysis

  15. Deformation

  16. Example

  17. Sound

  18. Sound Example

  19. Modal Decomposition

  20. Linearization

  21. Normalize for Mass

  22. Diagonalize

  23. Modal Decomposition

  24. Individual Modes

  25. Fast Computation

  26. PS 2 Example

  27. Sound Examples

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