• Slides (PDF)
  

• Download and install SideFX Houdini Apprentice (registration required)
• Start Houdini readings and tutorials in Homework #1
  

• Slides (PDF)
  
• Houdini project file (hipnc)
  
• Houdini learning curve (now with server ;)
  

• Slides (PDF)
  
• Houdini project file (hipnc)
• Extra: platonicness.hipnc
  

• Slides (PDF)
• Particle system dynamics (read Witkin course notes, slides)
• Numerical integration
• Particle collisions
  
• Energy-based modeling of forces
  
• Houdini example: particles.hipnc
  
• Particles bouncing on a plane
• Particles inside a convex domain
• Particles inside an SDF domain
• Particles attached to an SDF surface using damped springs <oh, my>
  

References:

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

• Slides (PDF)
• See video recording for live examples
  

• 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
• Houdini Example: Surface 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)

• 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.

• David Baraff and Andrew Witkin, Physically Based Modeling, Online SIGGRAPH 2001 Course Notes, 2001.
• Rigid Body Simulation (notes, slides)
• Two-body impulse calculation: See Baraff course notes.
• Euler's equations for dynamics of a single rigid body in body coords (wiki)
• Houdini example of body-coordinate integration (eulerRBMotion.hipnc)
  
• 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.
• Related topics:
  
• Rigid damping (see "Position Based Dynamics" [Mueller et al. 2006])
  
• Rigid cloth zones (see [Bridson et al. 2002])
  
• Twist frame evaluation on elastic rods (see "Discrete Elastic Rods" [Bergou et al. 2008])

• Miklós Bergou, Max Wardetzky, Stephen Robinson, Basile Audoly, and Eitan Grinspun. 2008. Discrete Elastic Rods. In ACM SIGGRAPH 2008 papers (SIGGRAPH '08). Association for Computing Machinery, New York, NY, USA, Article 63, 1–12. https://doi.org/10.1145/1399504.1360662
  

• 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.
• Jonathan M. Kaldor, Doug L. James, and Steve Marschner. 2010. Efficient yarn-based cloth with adaptive contact linearization. In ACM SIGGRAPH 2010 papers (SIGGRAPH '10). Association for Computing Machinery, New York, NY, USA, Article 105, 1–10. https://doi.org/10.1145/1833349.1778842
• Cem Yuksel, Jonathan M. Kaldor, Doug L. James, and Steve Marschner. 2012. Stitch meshes for modeling knitted clothing with yarn-level detail. ACM Trans. Graph. 31, 4, Article 37 (July 2012), 12 pages. https://doi.org/10.1145/2185520.2185533
  
• Jonathan Leaf, Rundong Wu, Eston Schweickart, Doug L. James, and Steve Marschner. 2018. Interactive design of periodic yarn-level cloth patterns. ACM Trans. Graph. 37, 6, Article 202 (December 2018), 15 pages. https://doi.org/10.1145/3272127.3275105
• Kui Wu, Xifeng Gao, Zachary Ferguson, Daniele Panozzo, and Cem Yuksel. 2018. Stitch meshing. ACM Trans. Graph. 37, 4, Article 130 (August 2018), 14 pages. https://doi.org/10.1145/3197517.3201360
  
• Kui Wu, Hannah Swan, and Cem Yuksel. 2019. Knittable Stitch Meshes. ACM Trans. Graph. 38, 1, Article 10 (February 2019), 13 pages. https://doi.org/10.1145/3292481  [Interactive knitting demo]
• Vidya Narayanan, Kui Wu, Cem Yuksel, and James McCann. 2019. Visual knitting machine programming. ACM Trans. Graph. 38, 4, Article 63 (July 2019), 13 pages. DOI: https://doi.org/10.1145/3306346.3322995
  
• Rundong Wu, Joy Xiaoji Zhang, Jonathan Leaf, Xinru Hua, Ante Qu, Claire Harvey, Emily Holtzman, Joy Ko, Brooks Hagan, Doug James, François Guimbretière, and Steve Marschner. 2020. Weavecraft: an interactive design and simulation tool for 3D weaving. ACM Trans. Graph. 39, 6, Article 210 (December 2020), 16 pages. https://doi.org/10.1145/3414685.3417865

• Fernando De Goes and Doug L. James. 2017. Regularized Kelvinlets: Sculpting brushes based on fundamental solutions of elasticity. ACM Trans. Graph. 36, 4, Article 40 (July 2017), 11 pages.
  
• Fernando De Goes and Doug L. James. 2018. Dynamic Kelvinlets: Secondary motions based on fundamental solutions of elastodynamics. ACM Trans. Graph. 37, 4, Article 81 (July 2018), 10 pages.
  
• Fernando de Goes and Doug L. James. 2019. Sharp Kelvinlets: Elastic deformations with cusps and localized falloffs. In Proceedings of the 2019 Digital Production Symposium (DigiPro ’19). Association for Computing Machinery, New York, NY, USA, Article 2, 1–8.

• Google Slide deck link on Ed

• 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. [PDF]  [Slides]  [Video]  [Project Page] (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]
• Unified particle physics:
• Miles Macklin, Matthias Müller, Nuttapong Chentanez, Tae-Yong Kim, Unified Particle Physics for Real-Time Applications, ACM Transactions on Graphics (SIGGRAPH 2014), 33(4) [Slides] [PDF] [Video] [Project Page]
• 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)

• 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]
• APIC method [Jiang et al. 2015]

Slides

• Bridson, R. and Muller-Fischer, M. 2007. Fluid Simulation for Computer Animation: SIGGRAPH 2007 Course Notes, In ACM SIGGRAPH 2007 Courses.  [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)
• C. Jiang, C. Schroeder, A. Selle, J. Teran, A. Stomakhin, An Affine Particle-In-Cell Method, ACM Transactions on Graphics (SIGGRAPH 2015), 34(4), pp. 51:1-51:10, 2015. [PDF]
  
• Y. Zhu and R. Bridson, Animating sand as a fluid, ACM SIGGRAPH 2005. [PDF] [MOV]  (introduced PIC/FLIP to graphics)

• Material Point Method (MPM) overview
• Application to snow simulation
  
• Deformation gradient
• Elastic strain energy, forces, and gradients
  
• Multiplicative plasticity methodology; application to snow
  
• Grid force and gradient calculations
• Semi-implicit integration of velocities
• Deformation gradient update
• Grid and particle collision handling
• Slides (courtesy Craig Schroeder & Joseph Teran)
  
• Practical tips for making a minimum viable snow simulator
  

Material:

• Alexey Stomakhin, Craig Schroeder, Lawrence Chai, Joseph Teran, Andrew Selle, A Material Point Method for Snow Simulation, ACM Transactions on Graphics (SIGGRAPH 2013), 32(4), pp. 102:1-102:10, 2013. [PDF] [YouTube Video]
• Related Technical Document [PDF] (on derivatives)
  
• Craig Schroeder, "Practical notes on implementing derivatives", with [CODE].
• Chenfanfu Jiang, Craig Schroeder, Joseph Teran, Alexey Stomakhin, Andrew Selle, The Material Point Method for Simulating Continuum Materials, SIGGRAPH Course 2016. [PDF]
• Disney's Matterhorn simulator

• Zhang et al., Progressive Simulation for Cloth Quasistatics, ACM Transactions on Graphics (SIGGRAPH Asia 2022).
  
• Zhang et al., Progressive Shell Quasistatics for Unstructured Meshes, ACM Transactions on Graphics (SIGGRAPH Asia 2023)
  
• Xue et al., Improved Water Sound Synthesis using Coupled Bubbles, ACM Transactions on Graphics (SIGGRAPH North America 2023).

• General ideas: 
• Projecting particle motion to be rigid motion
• Deformation gradient & Polar decomposition
  
• Rigid-body shape matching
• Fast Lattice 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]

• 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.
• 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.
• 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.
• "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]

• 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.