DATE

TOPICS

SUPPLEMENTAL
MATERIALS

Jan21

Introduction

Readings:
 An interesting historical
perspective:
 Terzopoulos, D., Pltt, J., Barr, A., Zeltzer, D., Witkin,
A., and Blinn, J. 1989. Physically based
modeling: past, present, and future. In ACM SIGGRAPH 89
Panel Proceedings (Boston, Massachusetts, United States, July 31

August 04, 1989). SIGGRAPH '89. ACM Press, New York, NY, 191209.

Jan26

Review:
Tensor Calculus

Discussed differentiating the
following quantities with respect to particle position vectors, p_i:
 constant, c
 position, p_j
 vectors, (p_jp_k)
 distances, p_jp_k
 distance powers, p_jp_k^n
 dot products, (p_1p_0)^T (p_3p_2)
 cross products
 Example: hair bending energy derivative, E =
k*sin^2(theta/2) [handout]

Jan28

Particle
Systems

Material:
 Discussed Assignment #1 Particle Systems
 Symplectic
Euler integrator (a.k.a. semiimplicit Euler)
 Videos:
 David Baraff and Andrew Witkin, Physically
Based Modeling, Online
SIGGRAPH 2001 Course Notes, 2001.

Due
Sun Feb 15

Assignment
#1
MassSpring Particle Systems

Link
to assignment
webpage

Feb02

Symbolic
Code Generation and Differentiation

Material:
 Slides
(PDF)
 Foreshadowing:
 deformation mapping
 deformation gradient
 Polar decomposition
 NewtonSchulz iteration

Feb04

Implicit
Integration;
IMEX and other schemes

Material:
 David Baraff and Andrew Witkin, Physically
Based Modeling, Online
SIGGRAPH 2001 Course Notes, 2001.
 Implicit Methods (Baraff)
 ImplicitExplicit (IMEX)
integration schemes:
 Ascher, Ruuth, Wetton, ImplicitExplicit Methods for
TimeDependent Partial Differential Equations, SIAM J. Num.
Anal. 32, pp. 797823, 1995.
 Bernhard Eberhardt, Olaf Etzmuß, Michael
Hauth, ImplicitExplicit Schemes for Fast
Animation with Particle Systems, Computer Animation and
Simulation 2000, Proceedings of the EG Workshop in Interlaken, 2122
August, 2000.
 Example: "Going implicit on damping"

Feb09

Solving
Sparse Linear Systems

Material:
 Poisson's equation model problem
 Overview of space/time complexity results for Poisson's
equation
 Iterative methods for sparse linear systems
 Matrix splitting & iterative solution
 Basic Methods:
 GaussSeidel
 Successive overrelaxation (SOR)
 Krylov Subspace Methods
 Basic idea
 Conjugate Gradient Method
 Reference:

Feb11
Feb16
Feb18

Robust
Collision Processing

Material:
 Velocitylevel collision resolution
 Continuous collision detection
 2D (pointedge, spheresphere), and 3D (pointface,
edgeedge) tests
 Impulse resolution
 Supporting pin/trajectory constraints
 Inversemass matrix filtering
 Penalty forces
 Rigid cloth zones
References:
 Robert Bridson, Ronald P. Fedkiw, John Anderson, Robust Treatment of Collisions, Contact,
and Friction for Cloth Animation, ACM Transactions on Graphics,
21(3), July 2002, pp. 594603.
 David Baraff, Andrew P. Witkin, Large
Steps in Cloth Simulation, Proceedings
of SIGGRAPH 98, Computer Graphics Proceedings, Annual Conference Series,
July 1998, pp. 4354.
 X. Provot, Collision and selfcollision handling in cloth
model dedicated to design garment. Graphics Interface, 177–89, 1997. (first introduction of rigid cloth zones)
 Robust Treatment of Simultaneous Collisions, David Harmon,
Etienne Vouga, Rasmus Tamstorf, Eitan Grinspun, ACM Transactions on
Graphics, 27(3), August 2008, pp. 23:123:4. (equalityconstraint alternative to rigid
cloth zones)

Due
Sun
Mar 8

Assignment
#2
Robust Collision Processing
(a.k.a. "The Spaghetti Factory")

Material:
 See Spaghetti Factory contest results
 Starter code available from CMS

Feb23

Rigid
Body Simulation

Material:
 Rigid body concepts (position, orientation, linear/angular
velocity, momentum, inertia, etc.)
 Contact impulses
 Example: rigid zones for cloth
 Frictionless contacts:
 Nonpenetration constraints
 Velocitylevel constraints (see Baraff course notes for
acclerationlevel constraints)
 Linear Complementarity Problem (LCP)
References:
 David Baraff and Andrew Witkin, Physically
Based Modeling, Online
SIGGRAPH 2001 Course Notes, 2001.
 (see cloth references for rigid cloth zones)

Feb25
Mar02

Constrained
Dynamics

Material:
 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 halfexplicit) DAE integration
schemes
References:
 David Baraff and Andrew Witkin, Physically
Based Modeling, Online
SIGGRAPH 2001 Course Notes, 2001.
 Rony Goldenthal, David Harmon, Raanan Fattal, Michel
Bercovier, Eitan Grinspun, Efficient Simulation of Inextensible Cloth,
ACM Transactions on Graphics, 26(3), July 2007, pp. 49:149:7.
[ACM Digital Library link]

Mar02
Mar04

The
Conjugate Gradient Method

Material:
 Jonathan
Richard Shewchuk, An Introduction to the
Conjugate Gradient Method Without the Agonizing
Pain, August 1994. PDF
(516k, 58 pages)

Mar09

Rigid
Body Contact;
Projected GaussSeidel Solver

Material:
 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, Velocitybased shock propagation for
multibody dynamics animation, ACM Trans. Graph. 26, 2, Jun.
2007. (most similar to Mar09
lecture)

Mar11

Assignment
#3
Rigid Body Contact
(a.k.a. "The Jelly Bean Factory")

Material:
 See "Jelly Bean Factory" contest results
 Starter code available from CMS (soon)

Mar16
Mar18

March
Break


Mar23

Corotational
Finite Elements

Material:
 M. Müller, M. Gross, Interactive Virtual Materials,
in Proceedings of Graphics Interface (GI 2004), pp 239246, London,
Ontario, Canada, May 1719, 2004. [Video]
 J. Georgii and R. Westermann, Corotated Finite Elements Made Fast and
Stable, VRIPHYS Workshop in Virtual Reality Interactions and
Physical Simulations, 2008. [PDF] [Video]

Mar25

Shape
Matching Methods

Material:
 Matthias Müller, Bruno Heidelberger, Matthias
Teschner, Markus Gross, Meshless
deformations based on shape matching, ACM Transactions on
Graphics, 24(3), August 2005, pp. 471478. [ACM]
[PDF] [AVI]
 Alec R. Rivers, Doug L. James, FastLSM: Fast Lattice Shape Matching for
Robust RealTime Deformation, ACM Transactions on Graphics,
26(3), July 2007, pp. 82:182:6. [ACM] [PDF]
 Denis Steinemann, Miguel A. Otaduy, Markus Gross, Fast Adaptive Shape Matching Deformations,
ACM SIGGRAPH/Eurographics Symposium on Computer Animation, Dublin, July
79, 2008. [PDF] [AVI]

Mar30
Apr06

Passive
Rigid Motion Control

Material:
 Ronen Barzel , John F. Hughes , Daniel N. Wood, Plausible motion simulation for computer
graphics animation, Proceedings of the Eurographics workshop
on Computer animation and simulation '96, p.183197, December 1996,
Poitiers, France .
 Jovan Popovic,
Steven M. Seitz, Michael Erdmann, Zoran Popovic, Andrew P. Witkin, Interactive Manipulation of Rigid Body
Simulations, Proceedings of ACM SIGGRAPH 2000, Computer
Graphics Proceedings, Annual Conference Series, July 2000, pp. 209218.
 Stephen Chenney, D. A. Forsyth, Sampling
Plausible Solutions to MultiBody Constraint Problems, Proceedings
of ACM SIGGRAPH 2000, Computer Graphics Proceedings, Annual Conference
Series, July 2000, pp. 219228.
 Christopher D. Twigg, Doug L. James, ManyWorlds Browsing for Control of
Multibody Dynamics, ACM Transactions on Graphics, 26(3),
July 2007, pp. 14:114:8. [ACM] [PDF] [Software Demo]
 Christopher D. Twigg, Doug L. James, Backward Steps in Rigid Body Simulation,
ACM Transactions on Graphics, 27(3), August 2008, pp. 25:125:10.
[ACM] [PDF]
 C. O'Sullivan and J. Dingliana, Collisions and Perception, ACM
Trans. Graph. 20, 3 (Jul. 2001), 151168.

Apr1 
Assignment Q&A Session

Material:





Final
Project 
Webpage



Apr08
Apr13

Fluid
Animation

Materials:
 Jos Stam,
Stable Fluids, Proceedings of
SIGGRAPH 99, Computer Graphics Proceedings, Annual Conference Series,
August 1999, pp. 121128. [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. 1522. (introduces vorticity confinement forces)
 Bridson, R., Fedkiw, R., and MullerFischer, 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, 187. [Slides, Notes]

Apr15

Smoke
Control

Materials:
 Adrien Treuille, Antoine McNamara,
Zoran Popović, Jos Stam, Keyframe
Control of Smoke Simulations, ACM
Transactions on Graphics, 22(3), July 2003, pp. 716723. [paper]
[project]
[video]
Graphbib
page
 Antoine McNamara, Adrien Treuille,
Zoran Popović, Jos Stam, Fluid control using the adjoint method,
ACM Transactions on Graphics,
23(3), August
2004, pp. 449456.
[paper]
[project]
Graphbib
page
 Raanan Fattal, Dani Lischinski, Targetdriven
smoke animation, ACM Transactions
on Graphics, 23(3), August 2004, pp. 441448. [paper]
[project]
Graphbib
page

Apr20

FluidSolid
Coupling

Materials:
 Mark Carlson, Peter J. Mucha, Greg Turk, Rigid Fluid: Animating the Interplay
Between Rigid Bodies and Fluid, ACM Transactions on
Graphics, 23(3), August 2004, pp. 377384. [paper]
[project] [graphbib]
[ACM
Digital Library] (a really
simple way to add rigid bodies to a fluid simulation)
 William V. Baxter III, Ming C. Lin, Haptic
Interaction with Fluid Media, Graphics Interface 2004, May 2004,
pp. 8188.
 Eran Guendelman, Andrew Selle, Frank Losasso, Ronald
Fedkiw, Coupling water and smoke to thin deformable
and rigid shells, ACM
SIGGRAPH 2005 Papers, July 31August 04, 2005, Los Angeles, California.
[project]
 Nuttapong Chentanez, Tolga G. Goktekin, Bryan E.
Feldman, James F.
O'Brien, Simultaneous coupling of fluids and
deformable bodies,
Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer
animation, September 0204, 2006, Vienna, Austria. [project]
 Jeroen Molemaker, Jonathan M. Cohen, Sanjit Patel, Junyong
Noh, Low Viscosity Flow Simulations for Animation,
Symposium on Computer Animation 2008. [paper]
[video
(mpeg4)] [youtube]
 RobinsonMosher, A., Shinar, T., Gretarsson, J., Su, J. and
Fedkiw, R., Twoway Coupling of Fluids to Rigid and
Deformable Solids and Shells, SIGGRAPH 2008, ACM TOG 27,
46.146.9 (2008). [Videos: 1,
2,
3]

Apr22
Apr27

"Staggered
Projections"

Material:
 A good reference on convex
optimization:
 Stephen Boyd and Lieven Vandenberghe, Convex Optimization, Cambridge
University Press, 2004.
 Stanford lecture notes/book [PDF]

Apr29

Project
Presentations












































































