CLASS
DATE 
TOPICS

MATERIAL (supplements whiteboard) 
MonJan10

Introduction











TuJan 14

PBMIS overview


ThJan 16

1. Basic dynamics
2. Numerical integration


TuJan 21

No class. Read SIGGRAPH course notes.


ThJan23

1. Constraints
& stabilization
2. Collision detection

 Recap of Baraff & Witkin reading
 Constrained Dynamics
 Any introductory text on Lagrangian
mechanics, e.g., Goldstein or Marion & Thornton.
 Comment on Baumgarte stabilization (whiteboard)
 Ming
Lin's course notes on collision detection:
 Collision
Detection: Basics & Convex Polyhedra
 D. P. Dobkin and D. G. Kirkpatrick. Determining the
separation of preprocessed polyhedra: a unified approach. In Proc.
17th Int. Colloq. Automata, Languages, and Programming, Lect. Notes in
Comput. Sci., vol. 443, SpringerVerlag, pages 400413, 1990.
 ICOLLIDE:
Interactive and Exact Collision Detection for LargeScale Environments,
by Cohen, Lin, Manocha & Ponamgi, Proc. of ACM Symposium on
Interactive 3D Graphics, 1995.
 A Fast Procedure for
Computing the Distance between Objects in ThreeDimensional Space, by
E.
G. Gilbert, D. W. Johnson, and S. S. Keerthi, In IEEE Transaction of
Robotics and Automation, Vol. RA4:193203, 1988.
 Matthew
Moore , Jane Wilhelms, Collision
detection and response for computer animation, SIGGRAPH 88.
 Brian
Mirtich, VClip:
fast and robust polyhedral collision detection, ACM Transactions on
Graphics (TOG), v.17 n.3, p.177208, July 1998
 Fast Penetration Depth
Computation For Physicallybased Animation,Young J. Kim, Miguel
A. Otaduy, Ming C. Lin, Dinesh Manocha, ACM SIGGRAPH Symposium on
Computer Animation. pp. 2332, 2002.
 Collision
Detection: BVHs & Spatial Partitioning
 Interactive
Collision Detection, by P. M. Hubbard, Proc. of IEEE Symp on
Research Frontiers in Virtual Reality, 1993. (aka Sphere Treesgood
for
deformable objects)
 Efficient
collision detection using bounding volume hierarchies of kdops, by
J. Klosowski, M. Held, J. S. B. Mitchell, H. Sowizral, and K. Zikan,
IEEE Trans. on Visualization and Computer Graphics, 4(1):2137, 1998.
 Collision
Detection between Geometric Models: A Survey, by M. Lin and S.
Gottschalk, Proc. of IMA Conference on Mathematics of Surfaces
1998.
 OBBTree: A
Hierarchical Structure for Rapid Interference Detection, by S.
Gottschalk, M. Lin and D. Manocha, Proc. of ACM Siggraph, 1996.
 Rapid and
Accurate Contact Determination between Spline Models using ShellTrees,
by S. Krishnan, M. Gopi, M. Lin, D. Manocha and A. Pattekar, Proc. of
Eurographics 1998.
 Other references
 John
M. Snyder , Adam R. Woodbury , Kurt Fleischer ,
Bena Currin , Alan H. Barr, Interval
methods for multipoint collisions between timedependent curved
surfaces, Proceedings of SIGGRAPH 93, p.321334, September 1993.
(Check out the "Fruit Tracing" example... with a lobster!).
 John M. Snyder, An
interactive tool for placing curved surfaces without interpenetration,Proceedings
of ACM SIGGRAPH 95, p.209218,
September 1995.
 Collision detection software: Google
section; UNC
gamma software


Assignment #1

 Constrained Particle
Systems (Due Tuesday, Feb 11, 2003)
 Submit your
writeup, code and videos in your directory
off /afs/cs.cmu.edu/academic/class/15863s03

TuJan 28

Introduction to rigid body dynamics

 Recap of Baraff & Witkin reading
 Brief
slide comments (ppt)
 References:
 Goldstein, H., Classical
Mechanics, AddisonWesley, Reading, 1983.
 Featherstone, R., Robot Dynamics
Algorithms, Kluwer, Boston, 1987.
 R. M.
Murray, Z. Li, and S. S. Sastry, A Mathematical Introduction to
Robotic Manipulation, CRC Press, first edition, 1994. (See Chapter
1
handouts).
 Software:
 See Jeff Trinkle's page
on multibody dynamics. Includes a nice survey of simulation packages
and
projects.

ThJan 30

Rigid body dynamics
and contact

 Class
slides (ppt)
 References: (see also those from last class)
 David
Baraff, Curved
surfaces and coherence for nonpenetrating rigid body simulation,
Proceedings of ACM SIGGRAPH 94, Volume 24 , Issue 4 (August 1990).
 David Baraff, Fast
contact force computation for nonpenetrating rigid bodies, Proceedings of ACM SIGGRAPH
94, p.2334, July 1994.
 Brian Mirtich
, John Canny, Impulsebased
simulation of rigid bodies, Proceedings of the 1995 symposium on
Interactive 3D graphics, p.181ff., April 0912, 1995, Monterey,
California, United States.
 Brian Mirtich, Timewarp
rigid body simulation, SIGGRAPH 2000, pp. 193200, ACM SIGGRAPH,
2000.
 Paul
G. Kry and Dinesh K. Pai, Continuous
Contact Simulation for Smooth Surfaces, Transactions on Graphics,
Vol 22, No 1, January, 2003.
 References
on fast multibody forward dynamics algorithms:
 Featherstone, R., Robot
Dynamics Algorithms, Kluwer, Boston, 1987.
 D.
Baraff. Lineartime
dynamics using Lagrange multipliers. ACM SIGGRAPH 96, 137146,
1996.
 U. M.
Ascher, D. K. Pai and B. Cloutier, Forward
Dynamics, Elimination Methods, and Formulation Stiffness in Robot
Simulation. International Journal of Robotics Research, 16:6, pp.
749758, December 97.
 François Faure, Fast Iterative
Refinement of Articulated Solid Dynamics, IEEE Transactions on
Visualization and Computer Graphics, 5(3), pp. 268276, 1999.
 U. Ascher and P. Lin, Sequential
Regularization Methods for simulating mechanical systems with many
closed loops, SIAM J. Scient.
Comput. 21, 12441262, 1999.
 Interesting applications:
 Karl
Sims, Evolving virtual creatures, Proceedings
of ACM SIGGRAPH 94, p.1522, July 1994.
 Stephen Chenney, D. A.
Forsyth, Sampling
Plausible Solutions to MultiBody Constraint Problems, Proceedings
of ACM SIGGRAPH 2000. pp. 219228, 2000.
 Jovan Popović, Steven M.
Seitz,
Michael Erdmann, Zoran Popović, Andrew P. Witkin, Interactive
Manipulation of Rigid Body Simulations, Proceedings
of ACM SIGGRAPH 2000, pp. 209218, 2000.

TuFeb 4

Elasticity
fundamentals

 Class slides (ppt)
 References:
 Any text on (nonlinear) elasticity,
e.g.,
 Ogden, R.W., NonLinear Elastic
Deformations
 Atkin, R.J. & Fox, N., An
Introduction to the Theory of Elasticity
 Fung, Y.C., Foundations of Solid
Mechanics
 Timoshenko,
S.P. & Goodier, J.N., Theory of Elasticity
 Boundary integral formulation; Boundary
element method (BEM)

ThFeb 6

1. Elastostatic Green's functions
2. Capacitance Matrix Algorithm

 Blackbox (datadriven) introduction to linear
elastostatic models.
 Class
slides (ppt)
 Slide references:
 D. James and D. K. Pai, ArtDefo, Accurate
Real Time Deformable Objects, In Proceedings of ACM SIGGRAPH 99,
Annual Conference Series, pp. 6572, August 1999.
 D. James and D. K. Pai, A Unified Treatment
of Elastostatic and Rigid Contact Simulation for Real Time Haptics,
Hapticse, the Electronic Journal of Haptics Research, Vol.2, No. 1,
September 2001. (Defines Capacitance
Matrix Algorithm using discretizationabstracted Green's functions;
same
notation as in class)
 Other deformable references:
 Morten BroNielsen, Stephane
Cotin, Realtime
Volumetric Deformable Models for Surgery Simulation using Finite
Elements and Condensation, Computer Graphics Forum, 1996.
 Stéphane Cotin,
Hervé Delingette, Nicholas Ayache, Realtime
elastic deformations of soft tissues for surgery simulation, IEEE
Transactions on Visualization and Computer Graphics, 5 (1), 6273, 1999.
 Jeffrey Berkley et al., Banded
Matrix Approach to Finite Element Modeling for Soft Tissue Simulation,
Virtual Reality: Research, Development, and Application,
4:203212, 1999. (webpage)
 Lowrank updating references:
 William W. Hager, Updating the inverse of a
matrix, SIAM Review, 31, 221239, 1989.

TuFeb 11

Deformable models in graphics

 Survey of selected formative works on
deformation.
 Class
slides (ppt)
 References:
 Some geometric deformation refs:
 Alan H. Barr, Global
and Local Deformations of Solid Primitives, Computer Graphics
(Proceedings of SIGGRAPH 84). 18(3), pp. 2130, 1984.
 Thomas W. Sederberg, Scott R. Parry, FreeForm
Deformation of Solid Geometric Models, Computer Graphics
(Proceedings of SIGGRAPH 86). 20(4), pp. 151160, 1986.
 Sabine Coquillart, Extended
FreeForm Deformation: A Sculpturing Tool for 3D Geometric Modeling,Computer
Graphics (Proceedings of SIGGRAPH 90). 24(4), pp. 187196, 1990.
 William M. Hsu, John F. Hughes, Henry
Kaufman, Direct
manipulation of freeform deformations, Computer Graphics
(Proceedings of SIGGRAPH 92). 26(2), pp. 177184, 1992.
 Ron MacCracken and Kenneth I. Joy. Freeform
deformations with lattices of arbitrary topology. ACM SIGGRAPH 96,
pages 181–188. ACM Press, 1996.
 Karan Singh, Eugene L. Fiume, Wires:
A Geometric Deformation Technique, Proceedings of SIGGRAPH 98. pp.
405414, 1998.
 Some physically based deformation refs:
 Terzopoulos, D., Platt, J., Barr, A., and
Fleischer, K., Elastically
Deformable Models, ACM SIGGRAPH 87, 205214, 1987.
 John C. Platt, Alan H. Barr, Constraint
methods for flexible models, ACM SIGGRAPH Computer Graphics, June
1988.
 Demetri Terzopoulos, Andrew Witkin, Physically
Based Models with Rigid and Deformable Components, IEEE Computer
Graphics & Applications. 8(6), pp. 4151, 1988.
 Alex Pentland, John Williams, Good
Vibrations: Modal Dynamics for Graphics and Animation, Computer
Graphics (Proceedings of SIGGRAPH 89). 23(3), pp. 215222, 1989.
 Dimitri Metaxas, Demetri Terzopoulos, Dynamic
deformation of solid primitives with constraints, ACM SIGGRAPH
Computer Graphics, 26(2), p.309312, July 1992.
 David Baraff, Andrew Witkin, Dynamic
simulation of nonpenetrating flexible bodies, Computer Graphics
(Proceedings of SIGGRAPH 92). 26(2), pp. 303308, 1992.
 MariePaule Gascuel, An
implicit formulation for precise contact modeling between flexible
solids, ACM SIGGRAPH 93, p.313320, September 1993.
 Demetri Terzopoulos , Hong Qin, Dynamic
NURBS with geometric constraints for interactive sculpting, ACM
Transactions on Graphics (TOG), v.13 n.2, p.103136, April 1994.
 Petros Faloutsos, Michiel van de Panne,
Demetri Terzopoulos, Dynamic
FreeForm Deformations for Animation Synthesis, IEEE Transactions
on
Visualization and Computer Graphics. 3(3), pp. 201214, 1997.
 MariePaule CaniGascuel, Mathieu
Desbrun, Animation of Deformable Models Using Implicit Surfaces, IEEE
Transactions on Visualization and Computer Graphics. 3(1), pp. 3950,
1997.
 Sarah F. F. Gibson, 3D
Chainmail: a Fast Algorithm for Deforming Volumetric Objects, 1997
Symposium on Interactive 3D Graphics. pp. 149154, 1997.
 S. Gibson and B. Mirtich. A Survey of
Deformable Modeling in Computer Graphics, Tech. Report No.
TR9719,
Mitsubishi Electric Research Lab., Cambridge, MA, November 1997.

ThFeb13

Deformable models in graphics (cont'd)

 References:
 See previous class slides & references.
 Shabana, A., Dynamics of multibody systems,
Wiley, New York, 1989. (whiteboard)


Assignment
#2

 HAIL STORM! (Due Tuesday, March 11)
 HINT: Single barycentric point constraint
 Starter code is
located in
 /afs/cs.cmu.edu/academic/class/15863s03/pbmisA2_HailStorm_starterCode.zip

TuFeb 18

Collision detection
for deformable models

 Class
slides (ppt)
 References:
 My handout:
James, "Summary of Collision Detection Algorithms for Deformable
Models," unpublished, 2002.
 G. van den Bergen. Efficient Collision Detection of
Complex Deformable Models using AABB Trees. Journal of Graphics
Tools, 4(2):113, 1997.
 S. Cotin, H. Delingette,
and N. Ayache, Realtime
elastic deformations of soft tissues for surgery simulation, IEEE
Transactions on Visualization and Computer Graphics, 5 (1), 6273,
1999. (example using uniform space partitioning)
 Thomas Larsson and Tomas
AkenineMöller, Collision
Detection for Continuously Deforming Bodies, Eurographics 2001.
(Improved updating of AABBTrees)
 J. Brown, S. Sorkin, C.
Bruyns, J.C. Latombe, K. Montgomery, and M. Stephanides. RealTime
Simulation of Deformable Objects: Tools and Application. In Proceedings
of Computer Animation 2001, Seoul, Korea, November 78 2001. (example
of
updating a sphere tree with fixed topology)
 Leonidas Guibas, An Nguyen,
Daniel Russel, and Li Zhang. Collision Detection for Deforming
Necklaces. In Proceedings of the Eighteenth Annual Symposium on
Computational Geometry, pages 3342. ACM Press, 2002. (updating a
sphere
tree w/ temporal coherence)

ThFeb 20

NVIDIA lecture (by Cem Cebenoyan)


TuFeb
25

Deformable multibody systems


ThFeb 27

Sound
modeling

 Class slides
(ppt)
 References:
 Adam Stettner, Donald P.
Greenberg, Computer
Graphics Visualization For Acoustic Simulation, Computer Graphics
(Proceedings of SIGGRAPH 89). 23(3), pp. 195206, 1989.
 Tapio Takala, James Hahn, Sound
Rendering, Computer Graphics (Proceedings of SIGGRAPH 92). 26(2),
pp. 211220, 1992.
 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. 382395.
 Thomas A. Funkhouser, Patrick Min, Ingrid
Carlbom, RealTime
Acoustic Modeling for Distributed Virtual Environments, Proceedings
of SIGGRAPH 99. pp. 365374, 1999.
 Perry Cook, Physically
Based Parametric Sound Synthesis and Control, ACM SIGGRAPH Course
Notes, 2000.
 Nicolas Tsingos, Thomas Funkhouser, Addy
Ngan, Ingrid Carlbom, Modeling
Acoustics in Virtual Environments Using the Uniform Theory of
Diffraction, Proceedings of ACM SIGGRAPH 2001. pp. 545552, 2001.
 Kees van den Doel , Paul G. Kry , Dinesh
K. Pai, FoleyAutomatic:
Physically Based Sound Effects for Interactive Simulation and Animation,
SIGGRAPH 2001, p.537544, August 2001.
 James F. O'Brien , Perry R. Cook , Georg
Essl, Synthesizing
Sounds from Physically Based Motion, SIGGRAPH 2001, p.529536,
August 2001. (Project
page)
 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, ACM SIGGRAPH 2001,
p.8796, August 2001.
 Perry R. Cook, Real Sound
Synthesis for Interactive Applications, AK Peters, 2002.
 O'Brien, J. F., Shen, C., Gatchalian, C.
M., Synthesizing
Sounds from RigidBody Simulations, ACM SIGGRAPH 2002
Symposium on Computer Animation, San Antonio, Texas, July 2122, pp.
175182.
 Thomas Funkhouser, JeanMarc Jot, Nicolas
Tsingos, “Sounds
Good to Me!” Computational Sound for Graphics, Virtual Reality, and
Interactive Systems, ACM SIGGRAPH Course Notes, 2002.
 Software

TuMar
4 
Cloth modeling (by Chris Twigg)

 Class slides
(pdf)
 References:
 Xavier
Provot, Deformation
Constraints in a MassSpring Model to Describe Rigid Cloth Behavior,
Graphics Interface '95, pp. 147154, 1995.
 David Baraff and Andrew P.
Witkin, Large
Steps in Cloth Simulation, Proceedings of SIGGRAPH 98, pp. 4354,
1998.
 D. E. Breen, D. H. House,
P. H. Getto, A PhysicallyBased Particle Model of Woven Cloth, The
Visual Computer. 8(56), pp. 264277, 1992.
 David E. Breen, Donald H.
House, Michael J. Wozny, Predicting
the Drape of Woven Cloth Using Interacting Particles, Proceedings
of SIGGRAPH 94. pp. 365372, 1994.
 Robert Bridson, Ron Fedkiw,
and John Anderson, Robust
treatment of collisions, contact and friction for cloth animation,
Proceedings of SIGGRAPH 2002, pages 594603.
 KwangJin Choi and
HyeongSeok Ko. Stable
but responsive cloth, Proceedings of SIGGRAPH 2002, pages 604611,
2002.
 X. Provot, Collision
and Selfcollision Handling in Cloth Model Dedicated to Design, Computer
Animation and Simulation '97, pp. 177190, 1997.
 Martin Courshesnes, Pascal
Volino, Nadia MagnenatThalmann, Versatile
and Efficient Techniques for Simulating Cloth and Other Deformable
Objects, Proceedings of SIGGRAPH 95, pp. 137144, 1995.

ThMar
6

No class (midterm break)


TuMar
11

Hair and strandlike deformable models

 Course project discussion
 Class
slides (ppt)
 References:
 Featherstone, R., Robot
Dynamics Algorithms, Kluwer, Boston, 1987.
 Kenichi Anjyo, Yoshiaki Usami, Tsuneya
Kurihara, A
simple method for extracting the natural beauty of hair, Computer
Graphics (Proceedings of SIGGRAPH 92). 26(2), pp. 111120, 1992.
 Ronen Barzel, Faking Dynamics
of Ropes and Springs, IEEE Computer Graphics & Applications.
17(3), pp. 3139, 1997.
 N.MagnenatThalmann, S.Hadap, P.Kalra, State
of the Art in Hair Simulation, International Workshop on Human
Modeling and Animation, Seoul, Korea, Korea Computer Graphics Society,
pp. 39, June, 2002.
 Sunil Hadap, Nadia MagnenatThalmann, Modeling
Dynamic Hair as a Continuum, Computer Graphics Forum, Volume 20,
Issue 3, Eurographics 2001 Proceedings, Manchester, United Kingdom,
September 2001.
 Eric Plante, MariePaule Cani, Pierre
Poulin, Capturing
the Complexity of Hair Motion, GMOD numéro 1 volume 64 ,
january 2002.
 Johnny T. Chang, Jingyi Jin, Yizhou Yu, A
Practical Model for Hair Mutual Interactions, ACM SIGGRAPH
Symposium
on Computer Animation. pp. 7380, 2002.
 TaeYong Kim, Ulrich Neumann, Interactive
Multiresolution Hair Modeling and Editing, ACM Transactions on
Graphics. 21(3), pp. 620629, 2002.
 Dinesh K. Pai, STRANDS:
Interactive Simulation of Thin Solids using Cosserat Models,
Computer Graphics Forum. 21(3), pp. 347352, 2002.

ThMar
13

Attend lecture by Szymon Rusinkiewicz


TuMar 18 
Multiresolution deformable modeling:
Adaptive simulation

 Class slides (ppt)
 References:
 H. Yserentant, On the
multilevel splitting of finite element spaces, Numer. Math., 49 (1986),
pp. 379412. (related
pub)
 Yan Zhuang and John Canny, Realtime
Simulation of Physically Realistic Global Deformation, IEEE
Vis'99 Late Breaking Hot Topics. San Francisco, California. October
2429, 1999.
 Gilles Debunne, Mathieu Desbrun,
MariePaule Cani, Alan H. Barr, Dynamic
RealTime Deformations Using Space & Time Adaptive Sampling,
Proceedings of ACM SIGGRAPH 2001. pp. 3136, 2001.
 Xunlei Wu, Michael S. Downes, Tolga
Goktekin, Frank Tendick, Adaptive
Nonlinear Finite Elements for Deformable Body Simulation Using Dynamic
Progressive Meshes, Computer Graphics Forum. 20(3), pp. 349358,
2001.
 Steve Capell, Seth Green, Brian Curless,
Tom Duchamp, Zoran Popović, A
Multiresolution Framework for Dynamic Deformations, ACM SIGGRAPH
Symposium on Computer Animation. pp. 4148, 2002.
 Eitan Grinspun, Petr Krysl, Peter
Schröder, CHARMS:
A Simple Framework for Adaptive Simulation, ACM Transactions on
Graphics. 21(3), pp. 281290, 2002.

ThMar 20 
No class (SIGGRAPH
committee meeting) 

TuMar 25

No
class (Spring break)


ThMar
27 
No
class (Spring break) 

TuApr
1

Multiresolution deformable modeling:
Datadriven simulation

 Class slides (ppt)
 References:

ThApr
3

Fracture
and cutting

 References:
 Terzopoulos,
D. and Fleischer, K., Modeling
Inelastic Deformation: Viscoelasticity, Plasticity, Fracture, ACM
SIGGRAPH 88, 269278, 1988.
 James F. O'Brien , Jessica K. Hodgins, Graphical
Modeling and Animation of Brittle Fracture, Proceedings of the 26th
annual conference on Computer graphics and interactive techniques,
p.137146, July 1999.
 F. Ganovelli, P. Cignoni, C. Montani, R. Scopigno, Enabling Cuts
on Multiresolution Representation, The Visual Computer. 17(5), pp.
274286, 2001.
 Andrew Mor, Progressive Cutting
with Minimal New Element Creation of Soft Tissue Models for Interactive
Surgical Simulation, doctoral dissertation, tech. report
CMURITR0129, Robotics Institute, Carnegie Mellon University, 2001.
 James F. O'Brien ,
Adam W. Bargteil , Jessica K. Hodgins, Graphical Modeling
and Animation of Ductile Fracture, ACM Transactions on
Graphics (TOG), v.21 n.3, July 2002.

TuApr
8

1. Finite Element Method (FEM) details
2. ImplicitExplicit (IMEX)
schemes

 References:
 Explicit linear tetrahedral FEM material:
 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.
 Mathieu Desbrun, Peter
Schröder, Al Barr, Interactive
Animation of Structured Deformable Objects, Graphics Interface '99.
pp. 18, 1999.

ThApr
10

Conservation laws


TuApr
15

Conservation laws (cont'd)


ThApr
17

1. SemiLagrangian integration schemes
2. Smoke simulation

 References:
 Staniforth, A., and J. Cote, SemiLagrangian integration schemes for
atmospheric models  A review. Mon. Wea. Rev., 119,
22062223, 1991.
 Dale R. Durran, Numerical Methods for
Wave Equations in Geophysical Fluid Dynamics, SpringerVerlag, 465
pages, 1999. (See chapter 6)
 Jos Stam, Stable
Fluids, SIGGRAPH 99. pp. 121128, 1999.
 Fedkiw, R., Stam, J. and Jensen, H.W., Visual
Simulation of Smoke, SIGGRAPH 2001, pp. 2330, 2001.

TuApr
22

1. Level sets
2. Fluids and fire simulation

 References:
 Stanley J. Osher, Ronald P. Fedkiw, Level
Set Methods and Dynamic Implicit Surfaces, Springer Verlag, 1st
ed., 2002.
 Nick Foster, Ronald Fedkiw, Practical
Animation of Liquids, Proceedings of ACM SIGGRAPH 2001. pp. 2330,
2001.
 Douglas P. Enright, Stephen R. Marschner,
Ronald P. Fedkiw, Animation
and Rendering of Complex Water Surfaces, ACM Transactions on
Graphics. 21(3), pp. 736744, 2002.
 Duc Quang Nguyen, Ronald P. Fedkiw,
Henrik Wann Jensen, Physically
Based Modeling and Animation of Fire, ACM Transactions on Graphics.
21(3), pp. 721728, 2002.

TuApr
24 
Project presentations 

TuApr
29

No
class (ACM I3D) 

TuMay 6

Project
presentations 

FriMay 9

Projects Due


N/A

Primer
on numerical linear algebra

 References:
 James W. Demmel, Applied
Numerical Linear Algebra, SIAM, 1997. (Chapter 6: Iterative Methods for
Linear Systems)
 William L. Briggs, Van Emden
Henson, Steve F. McCormick, A
Multigrid Tutorial, SIAM, 2000. (See tutorial
slides)
