Time and location

Lecture: TR 1:30-3

Office hour: Levine 303 TR 3-4

General description

This course is designed to explore selected topics in physics-based simulation of different materials and natural phenomena, with a focus on computer graphics applications. Simulating solids and fluids realistically and efficiently is essential in modern visual effects, animations and video games. Common examples of simulation include splashing liquids, clothing dynamics, hair dynamics, muscle and flesh motion, sand and snow dynamics, melting lava etc. Most of these visually astonishing results widely used in the entertainment industry necessitate a combination of knowledge in tensor calculus, numerical linear algebra, numerical partial differential equations, continuum mechanics and physics. One focus of this seminar is to work through these crucial math and physics components. Besides attending lectures and presenting research papers, students also gain hands on experience through a course project that aims at state-of-the-art simulation techniques.

Prerequisites

Multivariable calculus and linear algebra; Matlab/C++ programming

Recommended but not required

Computer graphics, numerical methods, partial differential equation, continuum mechanics, experience with Houdini/Maya/3D-Max

Recommended Texts

1. Nonlinear Continuum Mechanics for Finite Element Analysis, by J. Bonet and R. Wood.

2. A First Course in Continuum Mechanics, by O. Gonzalez and A. Stuart.

3. Fluid simulation for computer graphics, by R. Bridson

Course project

A material point method snow/sand simulator.

(Week 1: 8/29, 8/31)

Notes: Vector algebra, Tensor
algebra 1

Exercise Download

Homework: Poisson disk (recommended finishing time September 10th)

(Week 2: 9/5, 9/7)

Notes: Tensor algebra 2, SVD

Reading: Eigenvalue problems

Homework: 2D and 3D SVD

(Week 3: 9/12, 9/14)

Notes: Directional derivative, Tensor Calculus

(Week 4: 9/19, 9/21)

Practice: Dimension independent C++ template programming

Notes: Interpolation kenerl and continuum mechanics frames

Homework: free fall of a MPM object

(Week 5: 9/26, 9/28)

Notes: Kinematics1

Reading: APIC

(Week 6: 10/3, 10/5(fall break))

Conservation of mass

(Week 7: 10/10, 10/12)

Invited talk: Tiantian Liu

Notes: Hyperelasticity

(Week 8: 10/17, 10/19)

Notes: ODE and force

Reading: Updated Lagrangian F update

(Week 9: 10/24, 10/26)

Snow plasticity(Reading)

Notes: Isotropic elasticity and singular values.