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This schedule will be updated as the course progresses. Lecture slides will be posted here after class.

**Reading for next class:**

“Integrals as Sums and Derivatives as Differences” (lecture notes from *Introduction to Numerical Analysis*)

**Reading for next class:**

“Differential Equation Basics” and “Particle Dynamics” from Witkin and Baraff (2001)

**Reading for next class:**

“Nonlinear Equations” from *Introduction to Numerical Analysis*

**Links:**

Jonathan Shewchuk, “An Introduction to the Conjugate Gradient Method Without the Agonizing Pain” (1994)

**Reading for next class:**

“Implicit Methods” from Witkin and Baraff

**Links:**

- Miles Macklin’s derivation of the spring force Jacobian (though he silently ignores ∂
**F**/∂**x**for the damping term) - My multivariable differentiation cheat sheet

**Reading for next class:**

Sec. 1–3 of “Constrained Dynamics” from Witkin and Baraff

**Reading for next class:**

Sec. 6–7 of “Rigid Body Dynamics” from Witkin and Baraff

**Links:**

- Hadap et al., “Collision Detection and Proximity Queries” (2004)
*SDFs for simple geometrical shapes:*“modeling with distance functions” by Inigo Quilez*Code for computing SDFs from meshes:*Christopher Batty’s*SDFGen**Using SDFs for collision processing:*Bridson et al., “Simulation of Clothing with Folds and Wrinkles” (2003), sec. 5*Proximity queries for convex objects:*van den Bergen, “Proximity Queries and Penetration Depth Computation on 3D Game Objects” (2001)

**Links:**

*Vertex-face and edge-edge tests:*Provot, “Collision and self-collision handling in cloth model dedicated to design garments” (1997) sec. 1 and Bridson et al., “Robust Treatment of Collisions, Contact and Friction for Cloth Animation” (2002) sec. 6*Sweep and prune:*Cohen et al., “I-COLLIDE: An Interactive and Exact Collision Detection System for Large-Scale Environments” (1995), sec. 4–5.1*Bounding volume hierarchies:*Teschner et al., “Collision Detection for Deformable Objects” (2005), sec. 2

**Reading for next class:**

Sec. 1–2 of “Rigid Body Dynamics” from Witkin and Baraff

**Reading for next class:**

- Bridson et al., “Robust Treatment of Collisions, Contact and Friction for Cloth Animation” (2002)
- Guendelman et al., “Nonconvex Rigid Bodies with Stacking” (2003)
- Catto, “Iterative Dynamics with Temporal Coherence” (2005)

**Reading for next class:**

Sec. 3.1–3.6 of “Kinematics” (lecture notes from *Continuum Mechanics*)

**Reading for next class:**

Ch. 1–3 of “Part 1: The classical FEM method and discretization methodology” (course notes from Sifakis and Barbič (2012))

Mid-semester course feedback form

**Reading for next class:**

Ch. 1–4 of “Part 1: The classical FEM method and discretization methodology” from Sifakis and Barbič (2012)

**Reading for next class:**

Ch. 1–2 of Bridson and Müller-Fischer’s *Fluid Simulation for Computer Animation* (2007)

**Reading for next class:**

Ch. 3–4 of Bridson and Müller-Fischer (2007)

**Next class:**

- Yuchen Luo: Irving et al., “Invertible Finite Elements for Robust Simulation of Large Deformation” (2004)
- Jung Nam: Barbič and James, “Real-Time Subspace Integration for St.Venant-Kirchhoff Deformable Models” (2005)

**Next class:**

- Mauricio Flores: Fedkiw et al., “Visual Simulation of Smoke” (2001)
- Analise Rodenberg: Zhu and Bridson, “Animating Sand as a Fluid” (2005)

**Reading for next class:**

Müller et al., “Particle-Based Fluid Simulation for Interactive Applications” (2003)

**Links:**

*A comprehensive survey on SPH-based fluid animation:*Ihmsen et al., “SPH Fluids in Computer Graphics” (2014)*SPH with an incompressibility constraint:*Bender and Koschier, “Divergence-Free Smoothed Particle Hydrodynamics” (2015)

**Next class:**

- Lake Chen: Foster and Fedkiw, “Practical Animation of Liquids” (2001)

**Next class:**

- Yuchen Luo: Yu and Turk, “Reconstructing Surfaces of Particle-Based Fluids Using Anisotropic Kernels” (2010)

**Links:**

*More about level sets:*See Bridson and Müller-Fischer (2007) Ch. 6*Particle level set method:*Enright et al., “Animation and Rendering of Complex Water Surfaces” (2002)*Preserving volume in Eulerian advection:*Chentanez and Müller, “Mass-Conserving Eulerian Liquid Simulation” (2012)*Mesh-based surface tracking:*Wojtan et al., “Physics-Inspired Topology Changes for Thin Fluid Features” (2010)*Dealing with subgrid features:*Bojsen-Hansen and Wojtan, “Liquid Surface Tracking with Error Compensation” (2013)*Boundary conditions:*Gibou et al., “A Second Order Accurate Symmetric Discretization of the Poisson Equation on Irregular Domains” (2001) sec. 3.1 and Batty et al., “A Fast Variational Framework for Accurate Solid-Fluid Coupling” (2007)*Surface tension on…**level sets:*Losasso et al., “Simulating Water and Smoke with an Octree Data Structure” (2004) sec. 6;*meshes:*Thürey et al., “A Multiscale Approach to Mesh-based Surface Tension Flows” (2010);*particles:*Akinci et al., “Versatile Surface Tension and Adhesion for SPH Fluids” (2013)

**Next class:**

- Mauricio Flores: Irving et al., “Volume-Conserving Finite Element Simulations of Deformable Models” (2007)
- Jung Nam: Bouaziz et al., “Projective Dynamics: Fusing Constraint Projections for Fast Simulation” (2014)

**Next class:**

- Analise Rodenberg: Stomakhin et al., “A Material Point Method for Snow Simulation” (2013)
- Lake Chen: Da et al., “Surface-Only Liquids” (2016)

**Reading for next class:** At least two of the following:

- Batty et al., “A Fast Variational Framework for Accurate Solid-Fluid Coupling” (2007)
- Kaufman et al., “Staggered Projections for Frictional Contact in Multibody Systems” (2008)
- Gast et al., “Optimization Integrator for Large Time Steps” (2015)

**Dec 6:**Optimization-based methods**Dec 8:**TBD**Dec 13:**Project presentations