0. Particle-based fluids
   
1. Position-based dynamics
   
2. Final project (student's choice)
   

• David Baraff and Andrew Witkin, Physically Based Modeling, Online SIGGRAPH 2001 Course Notes, 2001.
• Differential Equation Basics
• Particle System Dynamics
• Cloth and Fur Energy Functions

• David Baraff and Andrew Witkin, Physically Based Modeling, Online SIGGRAPH 2001 Course Notes, 2001.
• Differential Equation Basics
• Particle System Dynamics
  
• Cloth and Fur Energy Functions (preview of energy function usage)
• Videos:
• Particle Dreams by Karl Sims, 1988.

• Holonomic constraints, C(p)=0.
  
• Example: Bead on a wire
• Differentiating constraints w.r.t. time.
• Constraint Jacobian, J
• Lagrange multipliers, lambda, and constraint forces, J^T lambda
  
• Solving for Lagrange multipliers
• (Implicit constraint (and half-explicit) DAE integration schemes)
• Post-step projection schemes
• Position- vs velocity-based corrections
  
• Applications: Mechanical linkages, inextensibility constraints, incompressible flow, contact constraints

Written assignment: Particle systems with holonomic constraints

• David Baraff and Andrew Witkin, Physically Based Modeling, Online SIGGRAPH 2001 Course Notes, 2001.
• Constrained Dynamics (slides)
• Examples from Cloth Simulation:
• Rony Goldenthal, David Harmon, Raanan Fattal, Michel Bercovier, Eitan Grinspun, Efficient Simulation of Inextensible Cloth, ACM Transactions on Graphics, 26(3), July 2007, pp. 49:1-49:7.  [ACM Digital Library link]
• Jonathan M. Kaldor, Doug L. James, Steve Marschner, Simulating Knitted Cloth at the Yarn Level, ACM Transactions on Graphics, 27(3), August 2008, pp. 65:1-65:9.

• U.M. Ascher and L.R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM.
• E. Hairer and G. Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, 2nd edition, Springer, 1996. (See Chapter VII.(1-2) Differential-Algebraic Equations of Higher Index)

• Smoothed Particle Hydrodynamics (SPH)
• Matthias Müller, David Charypar, Markus Gross, Particle-based fluid simulation for interactive applications, 2003 ACM SIGGRAPH / Eurographics Symposium on Computer Animation (SCA 2003), August 2003, pp. 154-159.  [Video]
• Miles Macklin and Matthias Müller. Position Based Fluids. ACM Trans. Graph. 32, 4, Article 104 (July 2013), 12 pages. (other videos)
• Liu, G. Gui-Rong, and M. B. Liu. Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, 2003.    
  
• Wikipedia
• Takahiro Harada, Seiichi Koshizuka, Yoichiro Kawaguchi, Smoothed Particle Hydrodynamics on GPUs, Computer Graphics International, pp. 63-70, 2007.
• B. Solenthaler, R. Pajarola, Predictive-Corrective Incompressible SPH, ACM Transactions on Graphics, 28(3), July 2009, pp. 40:1-40:6. [PDF] [YouTube Video]
• SIGGRAPH fluids course: [SPH pages (pp. 83-86)]
  
• Bridson, R., Fedkiw, R., and Muller-Fischer, M. 2006. Fluid simulation: SIGGRAPH 2006 course notes, In ACM SIGGRAPH 2006 Courses (Boston, Massachusetts, July 30 - August 03, 2006). SIGGRAPH '06. ACM Press, New York, NY, 1-87.  [Slides, Notes]
• Robert Bridson, Fluid Simulation for Computer Graphics, A K Peters, 2008. [Book format]
  
• Coupling SPH and rigid-body simulations (advanced):
• N. Akinci, M. Ihmsen, G. Akinci, B. Solenthaler, M. Teschner, Versatile Rigid-Fluid Coupling for Incompressible SPH, ACM Trans. Graph. (SIGGRAPH Proc.), 2012. [PDF] [AVI]
  
• Isosurface extraction + rendering
• OpenVDB
• Ken Museth, A Flexible Image Processing Approach to the Surfacing of Particle-Based Fluid Animation , MEIS2013 Abstract (a good high-level summary of particle-based fluids surfacing)
  

• PA1 webpage
• Canvas link (starter code + submission)
  

• Blackboard
• Backward Euler method
• Stability analysis of forward & backward Euler schemes on test problem
• U.M. Ascher and L.R. Petzold, Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM.
• Backward Euler for particle systems
• Application to cloth simulation [BW98]
  
• David Baraff and Andrew Witkin, Physically Based Modeling, Online SIGGRAPH 2001 Course Notes, 2001.
• Implicit Methods (Baraff)
• Slides
• Lecture Notes
• David Baraff, Andrew P. Witkin, Large Steps in Cloth Simulation, Proceedings of SIGGRAPH 98, Computer Graphics Proceedings, Annual Conference Series, July 1998, pp. 43-54.
  
• Implicit-Explicit (IMEX) integration schemes:
  
• Ascher, Ruuth, Wetton, Implicit-Explicit Methods for Time-Dependent Partial Differential Equations, SIAM J. Num. Anal. 32, pp. 797-823, 1995.
• Bernhard Eberhardt, Olaf Etzmuß, Michael Hauth, Implicit-Explicit Schemes for Fast Animation with Particle Systems, Computer Animation and Simulation 2000, Proceedings of the EG Workshop in Interlaken, 21-22 August, 2000. 
• Example: "Going implicit on damping"

• constant, c
  
• position, p_j
• vectors, (p_j-p_k)
• distances, ||p_j-p_k||
• distance powers, ||p_j-p_k||^n
• functions of distance, W(||p_j-p_k||)
  
• dot products, (p_1-p_0)^T (p_3-p_2)
• cross products
• Example: hair bending energy derivative, E = k*sin^2(theta/2)  [handout] [Mathematica]
  

• Numerical differentiation (less appealing in higher dimensions)
  
• Automatic and symbolic differentiation (Wiki)
•  Mitsuba autodiff implementation links
  
• Symbolic derivatives with optimized codegen (Maple)
  
• Slides
• Timothy Langlois's writeup on Automatic Differentiation of Moving Least Squares [Code example]
• Other examples

• David Baraff and Andrew Witkin, Physically Based Modeling, Online SIGGRAPH 2001 Course Notes, 2001.
• Rigid Body Simulation (slides)

• Projecting particle motion to be rigid motion
  
• Rigid-body shape matching
• FastLSM
• Other methods (adaptive FastLSM; oriented particles)
  

• Matthias Müller, Bruno Heidelberger, Matthias Teschner, Markus Gross, Meshless deformations based on shape matching, ACM Transactions on Graphics, 24(3), August 2005, pp. 471-478. [ACM] [PDF] [AVI]
  
• Alec R. Rivers, Doug L. James, FastLSM: Fast Lattice Shape Matching for Robust Real-Time Deformation, ACM Transactions on Graphics, 26(3), July 2007, pp. 82:1-82:6. [ACM] [PDF]
• Denis Steinemann, Miguel A. Otaduy, Markus Gross, Fast Adaptive Shape Matching Deformations, ACM SIGGRAPH/Eurographics Symposium on Computer Animation, Dublin, July 7-9, 2008. [PDF] [AVI]
• Matthias Müller and Nuttapong Chentanez. Solid simulation with oriented particles. ACM Trans. Graph. 30, 4, Article 92 (July 2011), 10 pages, 2011. [ACM] [PDF] [MOVIE]

• Jan. Bender, Matthias. Müller, Miles. Macklin, Position-Based Simulation Methods in Computer Graphics, EUROGRAPHICS Tutorial Notes, 2015, Zürich, May 4-8. (Course Notes)(Slides)
  
• M. Müller, B. Heidelberger, M. Hennix, J. Ratcliff, Position Based Dynamics, Proceedings of Virtual Reality Interactions and Physical Simulations (VRIPhys), pp 71-80, Madrid, November 6-7 2006, Best Paper Award, PDF, (video), (slides)
• Miles Macklin, Matthias Müller, Nuttapong Chentanez: XPBD: Position-Based Simulation of Compliant Constrained Dynamics in Proceedings of ACM Motion in Games, San Francisco, October 2016
  [PDF][Slides][Video][Youtube] (An improved PBD approach)

• Jos Stam, Nucleus: Towards a Unified Dynamics Solver for Computer Graphics, 2009 Conference Proceedings: IEEE International Conference on Computer-Aided Design and Computer Graphics, pp. 1-11, 2009. (related talk)
  
• T. Jakobsen, Advanced Character Physics, Game Developer Conference, 2001. 
• Miles Macklin, Matthias Müller, Nuttapong Chentanez, and Tae-Yong Kim. 2014. Unified particle physics for real-time applications. ACM Trans. Graph. 33, 4, Article 153 (July 2014), 12 pages. [ACM link]
  
• Sofien Bouaziz, Sebastian Martin, Tiantian Liu, Ladislav Kavan, and Mark Pauly. 2014. Projective dynamics: fusing constraint projections for fast simulation. ACM Trans. Graph. 33, 4, Article 154 (July 2014), 11 pages. [ACM link] 
• Rahul Narain, Matthew Overby, George E. Brown, ADMM ⊇ Projective Dynamics: Fast Simulation of General Constitutive Models, ACM SIGGRAPH / Eurographics Symposium on Computer Animation (SCA), 2016.
  

• PA2 webpage
• Canvas link (starter code + submission)

• Final project page
• Proposal Due Thurs Nov 17 (in class)

Material:

• Demetri Terzopoulos, Kurt Fleischer, Modeling Inelastic Deformation: Viscoelasticity, Plasticity, Fracture,Computer Graphics (Proceedings of SIGGRAPH 88), August 1988, pp. 269-278.
  
• James F. O'Brien, Jessica K. Hodgins, Graphical Modeling and Animation of Brittle Fracture, Proceedings of SIGGRAPH 99, Computer Graphics Proceedings, Annual Conference Series, August 1999, pp. 137-146.
• James F. O'Brien, Adam W. Bargteil, Jessica K. Hodgins, Graphical Modeling and Animation of Ductile Fracture, ACM Transactions on Graphics, 21(3), July 2002, pp. 291-294.
• Neil Molino, Zhaosheng Bao, Ron Fedkiw, A virtual node algorithm for changing mesh topology during simulation, ACM Transactions on Graphics, 23(3), August 2004, pp. 385-392. 
  
• M. Müller, M. Gross, Interactive Virtual Materials, in Proceedings of Graphics Interface (GI 2004), pp 239-246, London, Ontario, Canada, May 17-19, 2004. (Video)
  
• Mark Pauly, Richard Keiser, Bart Adams, Philip Dutré, Markus Gross, Leonidas J. Guibas, Meshless animation of fracturing solids, ACM Transactions on Graphics, 24(3), August 2005, pp. 957-964. [ACM] (Video) [PDF]
  
• Hayley N. Iben, James F. O'Brien, Generating Surface Crack Patterns, 2006 ACM SIGGRAPH / Eurographics Symposium on Computer Animation, September 2006, pp. 177-186.
• Denis Steinemann, Miguel A. Otaduy, Markus Gross, Fast Arbitrary Splitting of Deforming Objects, 2006 ACM SIGGRAPH / Eurographics Symposium on Computer Animation, September 2006, pp. 63-72. (Video)
  
• Bao, Z., Hong, J.-M., Teran, J. and Fedkiw, R., Fracturing Rigid Materials, IEEE TVCG 13, 370-378 (2007).
  
• Eftychios Sifakis, Kevin G. Der, Ronald Fedkiw, Arbitrary Cutting of Deformable Tetrahedralized Objects,2007 ACM SIGGRAPH / Eurographics Symposium on Computer Animation, August 2007, pp. 73-80.
• Eric G. Parker and James F. O'Brien, Real-Time Deformation and Fracture in a Game Environment, In Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Computer Animation, pages 156–166, August 2009.
• Su, J., Schroeder, C. and Fedkiw, R., Energy Stability and Fracture for Frame Rate Rigid Body Simulations,ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA), edited by Eitan Grinspun and Jessica Hodgins, pp. 155-164 (2009).
  
• Changxi Zheng, Doug L. James, Rigid-Body Fracture Sound with Precomputed Soundbanks, ACM Transactions on Graphics, 29(4), July 2010, pp. 69:1-69:13.
• M Müller, N Chentanez, TY Kim, Real time dynamic fracture with volumetric approximate convex decompositions, ACM Transactions on Graphics (TOG), 2013. [Video] 
  
• Oleksiy Busaryev, Tamal K. Dey, and Huamin Wang. 2013. Adaptive fracture simulation of multi-layered thin plates. ACM Trans. Graph. 32, 4, Article 52 (July 2013). [Video]
• Zhili Chen, Miaojun Yao, Renguo Feng, and Huamin Wang. 2014. Physics-inspired adaptive fracture refinement. ACM Trans. Graph. 33, 4, Article 113 (July 2014). [ACM]
• Yufeng Zhu, Robert Bridson, and Chen Greif, Simulating Rigid Body Fracture with Surface Meshes, Transactions on Graphics (Proc. ACM SIGGRAPH 2015).
  
• David Hahn and Chris Wojtan, High-Resolution Brittle Fracture Simulation with Boundary Elements, ACM Trans. Graph. 34, 4, Article 151 (July 2015).
• David Hahn and Chris Wojtan, Fast approximations for boundary element based brittle fracture simulation, ACM Trans. Graph. 35, 4, 104 (SIGGRAPH 2016).
  
• A recent review of fracture in graphics:
• L Muguercia, C Bosch, G Patow, Fracture modeling in computer graphics, Computers & Graphics, 2014.

• General discussion of rigid-body contact principles (contact constraints & impulses, restitution, Coulomb friction, maximal dissipation principle, Signorini-Fichera condition, connection with constrained optimization & KKT conditions, etc.), and methods such as impulse-based [Guendelman et al. 2003] and constraint-based [Erleben et al. 2007; Kaufman et al. 2008] solvers.
• Two-body impulse calculation: See Baraff course notes:
• David Baraff and Andrew Witkin, Physically Based Modeling, Online SIGGRAPH 2001 Course Notes, 2001.
• Rigid Body Simulation (slides)
• Excellent recent review:
• Jan Bender, Kenny Erleben and Jeff Trinkle, Interactive Simulation of Rigid Body Dynamics in Computer Graphics, Computer Graphics Forum, Volume 33, Issue 1, pages 246–270, February 2014, DOI: 10.1111/cgf.12272. 
  
• Impulse-based contact solvers: 
  
• Brian Mirtich, John Canny, Impulse-based Simulation of Rigid Bodies, 1995 Symposium on Interactive 3D Graphics, April 1995, pp. 181-188. 
  
• Eran Guendelman, Robert Bridson, Ronald P. Fedkiw, Nonconvex Rigid Bodies With Stacking, ACM Transactions on Graphics, 22(3), July 2003, pp. 871-878. [an iterative impulse-based solver]
• Projected Gauss-Seidel solver:
• K. Erleben, Stable, robust, and versatile multibody dynamics animation. Ph.D. thesis, Department of Computer Science, University of Copenhagen, Denmark, 2005. [avi movie]
  
• K. Erleben, Velocity-based shock propagation for multibody dynamics animation, ACM Trans. Graph. 26, 2, Jun. 2007.
• Projected Jacobi solver:
• Richard Tonge, Feodor Benevolenski, Andrey Voroshilov, Mass Splitting for Jitter-Free Parallel Rigid Body Simulation, ACM Trans. Graphics (SIGGRAPH 2012), 31(4), 2012.
  
• SIAM Review of rigid-body contact:
• D.E. Stewart, Rigid-body dynamics with friction and impact, SIAM Review, volume 42, 2000.
• "Staggered Projections" method:
  
• Danny M. Kaufman, Shinjiro Sueda, Doug L. James, Dinesh K. Pai, Staggered Projections for Frictional Contact in Multibody Systems, ACM Transactions on Graphics, 27(5), December 2008, pp. 164:1-164:11.
• A good reference on convex optimization:
• Stephen Boyd and Lieven Vandenberghe, Convex Optimization, Cambridge University Press, 2004.
• Stanford lecture notes/book [PDF]

• Navier-Stokes equations; Euler equations for inviscid fluids
  
• Advection; semi-Lagrangian methods
  
• Splitting schemes
  
• Incompressibility constraint & divergence-free flow
• Helmholtz-Hodge decompositions; pressure projection
  
• PIC/FLIP methods [Zhu & Bridson 2005]
  

• Bridson, R., Fedkiw, R., and Muller-Fischer, M. 2006. Fluid simulation: SIGGRAPH 2006 course notes, In ACM SIGGRAPH 2006 Courses (Boston, Massachusetts, July 30 - August 03, 2006). SIGGRAPH '06. ACM Press, New York, NY, 1-87.  [Slides, Notes] (main reference for class)
  
• Robert Bridson, Fluid Simulation for Computer Graphics, A K Peters, 2008
• Jos Stam, Stable Fluids, Proceedings of SIGGRAPH 99, Computer Graphics Proceedings, Annual Conference Series, August 1999, pp. 121-128.  [Slides and notes]
• Ronald Fedkiw, Jos Stam, Henrik Wann Jensen, Visual Simulation of Smoke, Proceedings of ACM SIGGRAPH 2001, Computer Graphics Proceedings, Annual Conference Series, August 2001, pp. 15-22.  (introduces vorticity confinement forces)

• Fernando de Goes (Pixar Research Group)

Material:

Power Particles: An incompressible fluid solver based on power diagrams
de Goes, Wallez, Huang, Pavlov, Desbrun
SIGGRAPH / ACM Transactions on Graphics (2015)
preprint video I video II dl.acm

• Come to class prepared to discuss & work on your final project
• Bring questions
  

• Ken Perlin and Eric Hoffert, Hypertexture, 1989 Computer Graphics (proceedings of ACM SIGGRAPH Conference), Vol. 22, No. 3. (Ken's write-up)
  
• Jos Stam and Eugene Fiume. 1993. Turbulent wind fields for gaseous phenomena. In Proceedings of the 20th annual conference on Computer graphics and interactive techniques (SIGGRAPH '93). ACM, New York, NY, USA, 369-376. 
  
• Ronald Fedkiw, Jos Stam, Henrik Wann Jensen, Visual Simulation of Smoke, Proceedings of ACM SIGGRAPH 2001, Computer Graphics Proceedings, Annual Conference Series, August 2001, pp. 15-22.  (introduces vorticity confinementforces)
• Jerry Tessendorf, Simulating Ocean Water, SIGGRAPH course notes, 2002. [Slides 2004]
  
• Frequency-domain methods commonly used for water wave simulation, e.g., NVIDIA WaveWorks.
• F. Neyret, Advected textures, In Proc. ACM SIGGRAPH/Eurographics Symp. Comp. Anim. (2003), pp. 147–153.
  
• Andrew Selle, Nick Rasmussen, Ronald Fedkiw, A vortex particle method for smoke, water and explosions, ACM SIGGRAPH 2005 Papers, July 31-August 04, 2005.
  
• Robert L. Cook and Tony DeRose. 2005. Wavelet noise. ACM Trans. Graph. 24, 3 (July 2005), 803-811. [ACM]
• Alexander Goldberg, Matthias Zwicker, Frédo Durand, Anisotropic noise, ACM Transactions on Graphics (TOG), v.27 n.3, August 2008.
• Robert Bridson, Jim Houriham, Marcus Nordenstam, Curl-noise for procedural fluid flow, ACM Transactions on Graphics (TOG), v.26 n.3, July 2007. (movie and public domain example code available.)
• Theodore Kim, Nils Thürey, Doug James, Markus Gross, Wavelet turbulence for fluid simulation, ACM Transactions on Graphics (TOG), v.27 n.3, August 2008. [ACM] (code available)
  
• H. Schechter, R. Bridson, Evolving sub-grid turbulence for smoke animation, Proceedings of the 2008 ACM SIGGRAPH/Eurographics Symposium on Computer Animation, July 07-09, 2008, Dublin, Ireland. [Movie]
  
• Rahul Narain, Jason Sewall, Mark Carlson, Ming C. Lin, Fast animation of turbulence using energy transport and procedural synthesis, ACM Transactions on Graphics (TOG), v.27 n.5, December 2008.
• Tobias Pfaff, Nils Thürey, Andrew Selle, and Markus Gross, Synthetic Turbulence using Artificial Boundary Layers,ACM SIGGRAPH Asia 2009 Papers, ACM Press, 2009.
  

• K. van den Doel and D. K. Pai, The Sounds of Physical Shapes, Presence: Teleoperators and Virtual Environments, 7:4, The MIT Press, 1998. pp. 382--395. 
  
• Kees van den Doel, Paul G. Kry, Dinesh K. Pai, FoleyAutomatic: Physically-Based Sound Effects for Interactive Simulation and Animation, Proceedings of ACM SIGGRAPH 2001, Computer Graphics Proceedings, Annual Conference Series, August 2001, pp. 537-544. [Video]
  
• Dinesh K. Pai, Kees van den Doel, Doug L. James, Jochen Lang, John E. Lloyd, Joshua L. Richmond, Som H. Yau, Scanning Physical Interaction Behavior of 3D Objects, Proceedings of ACM SIGGRAPH 2001, Computer Graphics Proceedings, Annual Conference Series, August 2001, pp. 87-96. [Video]
  
• James F. O'Brien, Perry R. Cook, Georg Essl, Synthesizing Sounds From Physically Based Motion, Proceedings of ACM SIGGRAPH 2001, Computer Graphics Proceedings, Annual Conference Series, August 2001, pp. 529-536.
• Perry R. Cook, Sound Production and Modeling, IEEE Computer Graphics & Applications, 22(4), July-August 2002, pp. 23-27.
• James F. O'Brien, Chen Shen, and Christine M. Gatchalian. Synthesizing sounds from rigid-body simulations. In The ACM SIGGRAPH 2002 Symposium on Computer Animation, pages 175–181. ACM Press, July 2002.
  
• Yoshinori Dobashi, Tsuyoshi Yamamoto, Tomoyuki Nishita, Real-Time Rendering of Aerodynamic Sound Using Sound Textures Based on Computational Fluid Dynamics, ACM Transactions on Graphics, 22(3), July 2003, pp. 732-740. [project page]
  
• Doug L. James, Jernej Barbić and Dinesh K. Pai, Precomputed Acoustic Transfer: Output-sensitive, accurate sound generation for geometrically complex vibration sources, ACM Transactions on Graphics, 25(3), pp. 987-995, July 2006, pp. 987-995.
  
• Changxi Zheng and Doug L. James, Harmonic Fluids, ACM Transaction on Graphics (SIGGRAPH 2009), 28(3), August 2009, pp. 37:1-37:12.
• Jeffrey Chadwick, Steven An, and Doug L. James, Harmonic Shells: A Practical Nonlinear Sound Model for Near-Rigid Thin Shells, ACM Transactions on Graphics (SIGGRAPH ASIA Conference Proceedings), 28(5), December 2009, pp. 119:1-119:10.
• Changxi Zheng and Doug L. James, Rigid-Body Fracture Sound with Precomputed Soundbanks, ACM Transactions on Graphics (SIGGRAPH 2010), 29(3), July 2010, pp. 69:1-69:13.
• Jeffrey Chadwick and Doug L. James, Animating Fire with Sound, ACM Transactions on Graphics, 30(4), August 2011.
• Jeffrey N. Chadwick, Changxi Zheng and Doug L. James, Precomputed Acceleration Noise for Improved Rigid-Body Sound, ACM Transactions on Graphics, August 2012.
• Steven S. An , Doug L. James, and Steve Marschner, Motion-driven Concatenative Synthesis of Cloth Sounds, ACM Transactions on Graphics, August 2012.
• Timothy R. Langlois and Doug L. James, Inverse-Foley Animation: Synchronizing rigid-body motions to sound, ACM Transactions on Graphics (SIGGRAPH 2014), 33(4), August 2014.