- Page 1: FEM Simulation of 3D Deformable Sol
- Page 5 and 6: Computer graphics and animation App
- Page 7 and 8: Deformable object simulations Task:
- Page 9 and 10: Real-time deformable objects • 30
- Page 11 and 12: Outline • Vega FEM • Introducti
- Page 13 and 14: Vega 13 • Free and open source (B
- Page 15 and 16: Deformable Models in Vega • Linea
- Page 17 and 18: Integrators in Vega • Implicit Ne
- Page 19 and 20: Materials in Vega • Linear materi
- Page 21 and 22: Sparse Linear Solvers: • Jacobi-p
- Page 23 and 24: Real-time Interaction 23
- Page 25 and 26: Fun Shing Sin, Daniel Schroeder, Je
- Page 27 and 28: Why PCG times depend on stiffness
- Page 29 and 30: Vega Live Demo 29 29
- Page 31 and 32: Online Course Notes: http://www.fem
- Page 33 and 34: Model Reduction + Faster computatio
- Page 35 and 36: Other Names for Projection-Based Mo
- Page 37 and 38: Model Reduction Outside of Computer
- Page 39 and 40: Outline • Vega FEM • Introducti
- Page 41 and 42: Notation: Deformation Vector (3D me
- Page 43 and 44: Linear Equations of Motion of 3D So
- Page 45 and 46: Columns of U are deformation basis
- Page 47 and 48: Linear Modes Linear Modes k = 4 sho
- Page 49 and 50: Linear Modes 49
- Page 51 and 52: Linear Modes are Shapes with the Le
- Page 53 and 54:
Linear Modes in Computer Graphics [
- Page 55 and 56:
Computing Linear Modes • Remove r
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• Works very well ARPACK • Writ
- Page 59 and 60:
Free-fly Modes 59
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Independent modal oscillators • I
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[James and Pai 2002] Linear modal s
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BD-Tree Collision Detection for Red
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Software for model reduction (by Je
- Page 69 and 70:
Live Demo: Building a Reduced Nonli
- Page 71 and 72:
Model Reduction of Nonlinear Deform
- Page 73 and 74:
3D Continuum Mechanics + FEM: • u
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Reduced equations of motion Substit
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Reduced internal forces: slow to ev
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How to select the basis ? Basis mus
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Motion basis from modal derivatives
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Basis Runtime simulation: Modal Der
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Comparison: Full simulation vs redu
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Modal Derivatives What load causes
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Simplified Heart (modal derivatives
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Nonlinear materials + reduction •
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Combining full simulation with mode
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Haptics (Greek; pertaining to the s
- Page 97 and 98:
Virtual assembly (aircraft geometry
- Page 99 and 100:
[Barbic, da Silva and Popovic 2009]
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[Barbic and Popovic 2008] Real-time
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Multibody dynamics with self-collis
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Model Reduction + FEM + Domain Deco
- Page 107 and 108:
Space Station dynamics: 75 fps, 250
- Page 109:
Acknowledgments • National Scienc