DATE

TOPICS

SUPPLEMENTAL
MATERIALS

Jan25

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.

Jan27

Review:
Tensor
Calculus

Discuss Particle System
Dynamics
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]


Particle
Systems

Material:

Feb1

Basic Integrators

Material:

Feb3

Assignment
#1
Particle Systems

Assignment #1 Homepage

Feb8

ParticleBased
Fluids

Material:
 Particle interaction force models
 Smoothed Particle Hydrodynamics (SPH)
 Matthias Müller, David Charypar,
Markus
Gross, Particlebased fluid
simulation for interactive applications, 2003 ACM SIGGRAPH /
Eurographics Symposium on Computer Animation (SCA 2003), August 2003, pp. 154159. [Video]
 Wikipedia
 Takahiro Harada, Seiichi Koshizuka, Yoichiro Kawaguchi, Smoothed
Particle Hydrodynamics on GPUs, Computer Graphics International,
pp. 6370, 2007.
 B. Solenthaler, R. Pajarola, PredictiveCorrective
Incompressible SPH, ACM Transactions on Graphics, 28(3), July 2009, pp. 40:140:6.
 Granular materials:
 Nathan Bell, Yizhou Yu,
and Peter J. Mucha,
ParticleBased Simulation of Granular Materials, ACM
SIGGRAPH/
Eurographics
Symposium
on
Computer
Animation
2005, [PDF]
[Video]
 Particle advection
 Isosurface extraction
 Rendering

Feb10

Implicit
Integration;
IMEX and other schemes

Material:
 Blackboard
 David Baraff and Andrew Witkin, Physically
Based Modeling, Online
SIGGRAPH 2001 Course Notes, 2001.
 Implicit Methods (Baraff)
 David Baraff, Andrew P. Witkin, Large
Steps
in
Cloth
Simulation, Proceedings
of
SIGGRAPH
98, Computer Graphics Proceedings, Annual Conference Series,
July
1998, pp. 4354.
 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"

Feb15
Feb17

Deformable
Models;
and
Corotational
Finite
Elements

Material:
 Blackboard
 Basic continuum mechanics
 Deformation (material and deformed coordinates,
deformation gradient)
 Polar decomposition (rotation, stretch)
 Strain (Green, linearized Cauchy)
 Strain Energy
 Stress and forces
 Tetrahedral finite elements
 Corotational finite elements
 References:
 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]




Feb22
Feb24
Mar01

Robust
Collision
Processing

Material:
 Velocitylevel collision resolution
 Continuous collision detection
 2D (pointedge, spheresphere), and 3D (pointface,
edgeedge) tests
 Impulse resolution
 Supporting pin/trajectory constraints
 Inversemassmatrix filtering
 Penalty forces
 Rigid cloth zones
References:
 Cloth related:
 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.
 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)
 X. Provot, Collision and selfcollision handling in cloth
model dedicated to design garment. Graphics Interface, 177–89, 1997. (first introduction of rigid cloth zones)
 General collision detection:
 M. Lin and
S.
Gottschalk, Collision detection between geometric
models: A survey, Proc. of IMA Conference on Mathematics of
Surfaces, volume 1, pp. 602608, 1998.
 P. Jimenez,
F. Thomas, and C. Torras, 3D collision detection: A survey,
Computers
&
Graphics,
Elsevier,
25(2),
pp.
269285,
2001.
 Gino Van Den
Bergen, Efficient collision detection
of complex deformable models using AABB trees, Journal of
Graphics Tools, 1998


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

Assignment
#2
Homepage

Mar03

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.
 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.
49:149:7.
[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. 65:165:9.

Mar08
Mar15

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:

Mar15
Mar17

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)

Mar17
Mar29
Mar31

Rigid
Body
Contact;
Projected GaussSeidel Solver

Material:
 SIAM Review of rigidbody
contact:
 Projected GaussSeidel solver (material for assignment):
 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 Mar17
lecture)

 Other
impulsebased
simulation
papers:
 Brian
Mirtich, John Canny, Impulsebased Simulation of
Rigid Bodies, 1995 Symposium on Interactive 3D Graphics, April 1995, pp. 181188.
 Eran
Guendelman, Robert Bridson, Ronald P. Fedkiw, Nonconvex Rigid Bodies With Stacking,
ACM
Transactions
on
Graphics,
22(3),
July 2003, pp. 871878. [another
iterative impulsebased solver]


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

Material:
 Starter code available from CMS

Mar22
Mar24

March
Break


Apr5
Apr7

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]

Apr7

Final
Project

Webpage
 Project proposal (PDF
format) [DUE: Wednesday April 7]

Apr12

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

Apr14

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]

Apr19

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]

Apr21
Apr26

No
Classes 

Apr28

Fracture

Material:

May3
May5

Project
Presentations

