DATE

TOPICS

MATERIALS

Wed Jan 26

Introduction
to
Computational Motion

Slides:
PDF
Read
for next class:
Agarwal, P. K., Guibas, L. J.,
Edelsbrunner, H.,
Erickson,
J., Isard,
M., HarPeled, S., Hershberger, J., Jensen, C., Kavraki, L., Koehl, P.,
Lin, M., Manocha, D., Metaxas, D., Mirtich, B., Mount, D.,
Muthukrishnan, S., Pai, D., Sacks, E., Snoeyink, J., Suri, S., and
Wolefson, O. 2002. Algorithmic issues in
modeling motion. ACM Comput. Surv. 34, 4 (Dec.
2002), 550572.

MonJan31
WedFeb2

EulerLagrange
Equations
of
Motion,
and
Computational
Complexity

Discussion: Algorithmic issues in
modeling motion [Agarwal et al. 2002].
References
for
Lagrangian dynamics:
 V.I. Arnold, Mathematical
Methods
of
Classical
Mechanics, Springer, 2nd edition, 1989. (more
mathematical text)
 H. Goldstein et al., Classical
Mechanics, Addison Wesley, 3rd edition, 2001. (standard ugrad
physics text)
 S.T. Thornton and J.B. Marion, Classical Dynamics of Particles and Systems,
Brooks
Cole,
5th
edition,
2003.
(easier
ugrad
physics
text)
Topics discussed:
 Nbody problems (allpairs complexity)
 Reducedcoordinate deformable bodies (spatial/integration
complexity)
 2D serial manipulator (recursive complexity)
Read for MonFeb7 class:
[Baraff & Witkin 1998]
 Post discussion comments on group before class.
Assignment
#1
for
Wed
Feb
9
(homework
due
in
class):
Regarding the
simplified Nbody planar serial manipulator
from class: Given joint
angles and
velocities, what is the
complexity of naive evaluation of joint
accelerations from the expanded EulerLagrange equations? Provide
evidence to support your claim using the equations.

MonFeb7

Deformable
Models:
Cloth Motion

Topics
discussed:
 Modeling cloth with energy terms
 Implicit integration
 Tensor calculus recap:
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
 ...
References:
 Baraff, D. and Witkin, A. 1998. Large steps in cloth simulation.
In Proceedings of the 25th Annual Conference on Computer Graphics and
interactive Techniques SIGGRAPH '98. ACM, New York, NY, 4354.
 Jonathan
Richard
Shewchuk,
An
Introduction to the
Conjugate Gradient Method Without the Agonizing
Pain, August 1994. PDF
(516k,
58
pages)
 Discussion group posts
Assignment #2 for Mon Feb 21 class (homework due
in class): Derive
forces/Jacobians for [Baraff
& Witkin 1998] (assignment (PDF)).

WedFeb9
MonFeb14

Rigid
Body
Dynamics

Topics
discussed:
 Rotational and rigid motion; kinematics and dynamics
 SO(3), Special Orthogonal group in 3D
 SE(3), Special Euclidean group in 3D
 Rigidbody motion
 Spatial velocity vectors (contravariant twists);
se(3); transformation
 Kinetic energy; inertia, principal axes
 Spatial forces (covariant wrenches); se*(3); transformation
 Velocity of contact points, and relation to twists
 Forces at contact points, and relation to wrenches
 NewtonEuler equations of motion
 Integrating rigidbody dynamics
 Deformable bodies; mode matrix, U; extensions
to framework
References:
 Murray, R. M., Sastry, S. S., and Zexiang, Li, A Mathematical Introduction to Robotic
Manipulation. 1st. CRC Press, Inc., 1994.
 See summary in appendix of:
 Ball's screw theory
 Ahmed A. Shabana, Dynamics of Multibody Systems,
Cambridge, 3rd ed, 2005.


Discussion:
Parallel
RigidBody Dynamics

Reference:

MonFeb14
WedFeb16

Robot
Dynamics
Algorithms

Topics discussed:
 Algorithms overview
 Forward and inverse kinematics
 Inverse dynamics (control)
 Forward dynamics (simulation)
 Notation
 Recurrence relations
 Recursive NewtonEuler Algorithm (RNEA)
 CompositeRigidBody Algorithm (CRBA)
 Usage in O(N^3) forward dynamics (CRBA + RNEA + dense
solve)
 ArticulatedBody Algorithm (ABA)
 a.k.a. "Featherstone's algorithm"
 O(N) forward dynamics
 Closedloop systems
 Constraints and fast solution methods
 Global analysis techniques
 Fast robot algorithms as sparse matrix methods
References:
 Roy Featherstone and David Orin, Robot Dynamics: Equations and Algorithms,
Proc.
IEEE
Int.
Conf.
Robotics
&
Automation,
San
Francisco,
CA,
2000,
pp.
826–834.
(an
excellent
review)
 Roy Featherstone, Robot Dynamics Algorithms,
Kluwer Academic Publishers, 1987. (classic bookhighly readable)
 Roy Featherstone, A DivideandConquer ArticulatedBody
Algorithm for Parallel O(log(n)) Calculation of RigidBody Dynamics.
Part 1: Basic Algorithm, The International Journal of
Robotics Research, Vol. 18, No. 9, 867875, 1999. (has good
appendix on spatial notation)
 Roy Featherstone, Rigid
Body Dynamics Algorithms, Boston: Springer, 2007.
 E. Kokkevis, Practical Physics for Articulated Characters,
Proc.
of
Game
Developers
Conference
(GDC),
2004.
(good
overview
of
system
integration
issues
for
ABA,
e.g.,
handling
contact
and
constraints)
 David Baraff, LinearTime Dynamics using
Lagrange Multipliers, Proceedings of
SIGGRAPH 96, Computer Graphics
Proceedings, Annual Conference Series, August
1996, pp. 137146.
 Robot
dynamics, Scholarpedia page.
 D.K. Pai, STRANDS: Interactive Simulation of Thin
Solids using Cosserat Models, Computer Graphics Forum,
21(3), pp. 347352, 2002.

MonFeb21

Discussion:
Articulated Body Algorithm (ABA)

Reference:

MonFeb21

Constrained
Dynamics
and
DifferentialAlgebraic
Equations
(DAEs)

References
for
DifferentialAlgebraic
Equations
(DAEs):
Topics discussed:
 Constrained Lagrangian dynamics
(CLD)
 Holonomic constraints
 Constraintaugmented Lagrangian
 Examples, e.g., pendulum
 DAE systems
 Differentiation index
 Structure of index1, 2, and 3 DAE systems
 Index reduction by differentiation
 Driftoff phenomena

WedFeb23

Integrating
Constrained Dynamics

Topics
discussed:
 Constrained Lagrangian dynamics in index1, 2, 3 and GGL
DAE forms
 Solving for Lagrange multiplier from index1 form.
 Constraint stabilization:
 Baumgarte's method; modified Lagrange multiplier
 Projection (position, velocity)
 Implicit integration of DAEs (for stiff problems)
 General DAEs, and semiexplicit index1 DAEs
 Backwards Euler
 BDF and multistep methods
 Halfexplicit RungeKutta methods
 Methods for ODEs on manifolds
 Poststabilization
 Coordinate projection (c.f. coordinate resetting)
 Hamiltonian dynamics; energy conservation
 Symplectic integrators w/ constraints (SHAKE & RATTLE)
Additional CLD reference:
David Baraff and Andrew Witkin, Physically Based Modeling,
Online SIGGRAPH 2001 Course Notes, 2001. 
WedFeb23

Discussion
(Andrew
Spielberg)

Reference:
 Hayley N. Iben,
James F. O'Brien, and Erik D. Demaine. "Refolding
Planar
Polygons". Discrete and Computational Geometry,
41(3):444–460,
April 2009.

MonFeb28

Frictional
Contact

Topics
discussed:
 Impact models; restitution coefficient
 Nonpenetration constraints
 Linear complementarity problems (LCP); QP
formulations; Dantzig's algorithm
 Friction
 Painleve's paradox; frictional indeterminacy;
frictional inconsistency; the importance of impulses
 Velocitylevel contact formulation
 The myth of "contact points"; distributed friction
forces;
planar sliding; center of friction
 Contacting multibody systems
 Nonpenetration constraints; SignoriniFichera
condition
 Maximal dissipation principle
 "Staggered Projections" contact algorithm
 Iterative solvers; projected GaussSeidel methods
References:
 D.E. Stewart, RigidBody Dynamics with Friction and Impact,
SIAM
Review,
42(1),
pp.
339,
2000.
 D. Baraff, Fast contact force computation for
nonpenetrating rigid bodies, Computer Graphics Proceedings,
Annual Conference Series: 2334, 1994. (cover's Dantzig's algorithm)
 D. Baraff, Coping with
friction for nonpenetrating rigid body simulation, Computer
Graphics 25(4): 3140, 1991. (cover's frictional indeterminacy &
inconsistency)
 Danny M. Kaufman, Shinjiro Sueda, Doug L. James and Dinesh
K. Pai, Staggered Projections for Frictional
Contact in Multibody Systems, ACM Trans. Graph.(Proc.
SIGGRAPH Asia), 27, 2008.
 Brian Mirtich, Impulsebased Dynamic Simulation of Rigid
Body Systems, Ph.D. thesis, UC Berkeley, 1996.
 Eran Guendelman , Robert Bridson , Ronald Fedkiw, Nonconvex
rigid
bodies
with
stacking, ACM Transactions on Graphics (TOG),
v.22 n.3, July 2003 [doi>10.1145/882262.882358] (good example of a velocitylevel
iterative contact solver)
 Kenny Erleben, Velocitybased shock
propagation for multibody dynamics animation, ACM Transactions on Graphics, 26(2), June 2007, pp. 12:112:20. (good summary of a velocitylevel
projected GaussSeidel contact solver)
 Christopher D. Twigg, Doug L. James, Backward Steps in Rigid Body Simulation, ACM Transactions on Graphics, 27(3), August 2008, pp. 25:125:10.
(see for summary of
velocitylevel contact problem)

MonFeb28

Discussion
(Chuck
Moyes)

Reference:

WedMar2

Frictional
Contact
(cont'd)


WedMar2

Discussion
(Jeffrey
Ames)

Reference:

MonMar7

No class (PhD Visit Day)
> Project planning day

Work
on
project
proposals:
 Hand in proposal in
Wednesday Feb 9 class.
 Get feedback then get
cracking.

WedMar9

Course
Project
Discussion

Agenda:
 Discussion of [Parker and O'Brien 2009]
 Submit project proposals
 Informal discussion of proposed course projects; revisions
 BOOM
Showcase at 4pm

WedMar9

Discussion
(Himanshu
Bhatia
&
Jonathan
Hirschberg)

Reference:

MonMar14

Friction
Contact
(cont'd):
Staggered Projections


WedMar16
MonMar28
WedMar30

Incompressible
Flow

Topics
discussed:
 Advection; upwind differencing; ENO schemes
 Incompressibility constraint
 NavierStokes equation
 MAC grid discretization; interpolation and
averaging; upwinding
 Timestepping schemes (Eulerian, and semiLagrangian)
 Projection to divergencefree velocity
 Poisson equation; discretization; compatibility
condition; PCG solution
 DAE view of incompressible flow
 Higherorder semiLagrangian schemes; monotone
interpolation; BFECC; CIP and USCIP
Reference:
 S. Osher and R. Fedkiw, Level Set Methods and Dynamic Implicit
Surfaces, Applied Mathematical Sciences, volume 153,
SpringerVerlag, 2003.
 U.M. Ascher and L.R. Petzold, Computer
Methods
for
Ordinary
Differential
Equations
and
DifferentialAlgebraic
Equations, SIAM.
 Jos Stam,
Stable Fluids, Proceedings of
SIGGRAPH 99, Computer Graphics Proceedings, Annual Conference Series,
August 1999, pp. 121128.
 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]
 Foster, N. and Fedkiw, R., Practical Animation of Liquids,
SIGGRAPH 2001, 1522 (2001).
 Enright, D., Marschner, S. and Fedkiw, R., Animation and Rendering of Complex Water
Surfaces,
SIGGRAPH 2002, ACM TOG 21, 736744 (2002).
 Yongning Zhu , Robert Bridson, Animating
sand
as
a
fluid, ACM Transactions on Graphics (TOG), v.24 n.3, July
2005. (Discusses PIC and FLIP hybrid particle/grid methods)
 Higherorder advection schemes:
 BFECC and MacCormack methods:
 Byungmoon Kim, Yingjie Liu, Ignacio Llamas, Jarek
Rossignac,
Advections
with Significantly Reduced Dissipation and Diffusion, IEEE
Transactions on Visualization and Computer Graphics, Volume 13, Issue
1, Pages 135144, 2007. video(DivX)
 Selle, A., Fedkiw, R., Kim, B., Liu, Y., and Rossignac,
J. 2008. An Unconditionally Stable MacCormack Method.
J. Sci. Comput. 35, 23 (Jun. 2008), 350371.
 Methods with small stencils (constrained interpolation
profile (CIP)):
 A projection method to approximate complex boundaries:
 Multigrid Poisson solver
 A.
McAdams,
E. Sifakis,
J. Teran, A Parallel Multigrid Poisson Solver for
Fluids Simulation on Large Grids, ACM SIGGRAPH/Eurographics
Symposium on Computer Animation (SCA) edited by M. Otaduy and Z.
Popovic, pp.110, 2010. [PDF] [Video+Code]
 A
coarsegrid
Poisson
solver

MonMar21
WedMar23

Spring Break (No classes)


MonMar28

Discussion
(Ivaylo
Boyadzhiev)

Hadrien
Courtecuisse,
Hoeryong
Jung,
Jérémie
Allard,
Christian
Duriez,
Doo
Yong
Lee,
Stéphane
Cotin,
GPUbased
RealTime Soft Tissue Deformation with Cutting and Haptic Feedback, Progress in Biophysics and
Molecular Biology 103, 23, pages 159–168  December 2010,
doi:10.1016/j.pbiomolbio.2010.09.016, Special Issue on Soft Tissue
Modelling

WedMar30

Discussion
(Yunfeng
Bai)

Lentine,
M.,
Zheng,
W.,
and
Fedkiw,
R.,
A
Novel Algorithm for Incompressible Flow Using Only A Coarse Grid
Projection, SIGGRAPH 2010, ACM TOG 29, 4 (2010). [Video]

Mon4Apr

Project
Updates

Description:
 Each project group will give a short 5minute presentation
on their project topic, current results/progress, and goals for the
remaining month.

Wed6Apr
Mon11Apr

GradientDomain
Shape
and
Deformable
Motion
Modeling

References:
 Robert W. Sumner, Jovan Popović, Deformation transfer for triangle meshes,
ACM
Transactions
on
Graphics,
23(3),
August
2004,
pp.
399405.
 Robert W. Sumner, Matthias Zwicker, Craig Gotsman, Jovan
Popović, Meshbased Inverse Kinematics,
ACM Transactions on Graphics, 24(3), August 2005, pp. 488495.

Wed6Apr

Discussion
(Jiexun
Xu)

Geometric,
Variational Integrators for Computer Animation
L. Kharevych, Weiwei, Y. Tong, E. Kanso, J. E. Marsden, P.
Schröder, and Mathieu Desbrun
ACM/EG Symposium on Computer Animation 2006, pp. 4351 
Mon11Apr

Subspace
Deformation
(Pixar
style)

References:
 Mark Meyer, John Anderson, Key Point Subspace
Acceleration and Soft Caching, ACM
Transactions on Graphics, 26(3), July 2007, pp. 74:174:8.
 Pushkar Joshi, Mark Meyer, Tony DeRose,
Brian Green, Tom Sanocki, Harmonic Coordinates for
Character Articulation, ACM
Transactions on Graphics, 26(3), July 2007, pp. 71:171:9.

Wed13Apr
Mon18Apr

Collision
Detection,
and
Subspace Deformation Bounds

Topics
discussed:
 Bounding volumes (spheres, boxes, kDOPs, etc)
 Separating axis theorem
 Spacetime bounds
 Bounding moving points
 Bounding subspace deformations;
 Bounded Deformation Trees
 O(r) and O(1) updates
 Spheres, boxes, kDOPs
 Translational and affine/rotational models
References:
 Philip M. Hubbard. 1996. Approximating polyhedra with spheres for
timecritical collision detection. ACM Trans. Graph.
15, 3 (July 1996), 179210. DOI=10.1145/231731.231732
http://doi.acm.org/10.1145/231731.231732
 B. Gaertner, Fast and
Robust Smallest Enclosing Balls, Lecture Notes in Computer
Science, Springer, pp. 325338, 1999.
 Miniball
software, Smallest Enclosing Balls of Points  Fast and Robust in
C++.
 Doug L. James, Dinesh K. Pai, BDTree: Outputsensitive collision
detection for reduced deformable models, ACM Transactions on
Graphics, 23(3), August 2004, pp. 393398. [SIGGRAPH
Talk]
 M. Teschner et al., Collision Detection for Deformable Objects,
Eurographics
StateoftheArt
Report
(EGSTAR),
Eurographics
Association,
pages
119139,
2004.
 Jernej Barbič and Doug L. James, SixDoF haptic rendering of contact between
geometrically complex reduced deformable models, IEEE
Transactions on Haptics, 1(1):39–52, 2008. [Project page]
Assignment
for
Mon
May
9:
Building
on the affine motion model (described for spheres in class), propose a
tight 6DOP deformation bound that supports large rotations (is affine
invariant) and has an O(r) update cost for r displacement modes.

Wed13Apr 
Discussion
(Kevin
Matzen)

M.
Müller,
R.
Keiser,
A.
Nealen,
M.
Pauly,
M.
Gross, M.
Alexa, Point Based Animation of
Elastic, Plastic and Melting
Objects,
SCA 2004.
Videos:

Mon18Apr

Discussion
(Nathan
Lloyd
&
Greg
Sadowski)

Oktar Ozgen, Marcelo Kallmann, Lynnette Es Ramirez,
Carlos Fm Coimbra, Underwater cloth simulation
with fractional derivatives, ACM
Transactions on Graphics, 29(3), June 2010, pp. 23:123:9. 
Wed20Apr

Subspace
Dynamics;
PhysicsBased
Sound
Rendering

Topics discussed:
 Dimensional model reduction
 linear & nonlinear dynamics
 linear integration; IIR digital filter
 generalized eigenvalue problem; mass normalization
 Newmark integration
 full vs subspace
 explicit & implicit
 Reducedorder deformation force models
 exact reductions (linear, StVK)
 approximations (cubature)
 Reducedorder fluids
 Sound rendering
 rigid bodies
 nonlinear thin shells; mode coupling
References:
 S. R. Idelsohn and A. Cardona, A Reduction Method for Nonlinear Structural
Dynamic Analysis, Computer Methods in Applied Mechanics and
Engineering 49, 253279, 1985.
 A. A. Shabana, Theory of
Vibration (Volume II: Discrete and Continuous Systems),
SpringerVerlag, New York, NY, 1990.
 P. Krysl, S. Lall, and J.E. Marsden, Dimensional
model
reduction
in
nonlinear finite element dynamics of solids and
structures, Int. J. for Numerical Methods in Engineering, 51,
479504, 2001.
 Doug L. James, Dinesh K. Pai, DyRT: Dynamic Response Textures for Real
Time Deformation Simulation With Graphics Hardware, ACM
Transactions on Graphics, 21(3), July 2002, pp. 582585.
 Jernej Barbič and Doug L. James, RealTime Subspace Integration of
St.VenantKirchhoff Deformable Models, ACM Transactions on
Graphics (ACM SIGGRAPH 2005), 24(3), pp. 982990, August 2005, pp.
982990.
 Adrien Treuille, Andrew Lewis, Zoran Popović, Model reduction for realtime fluids,
ACM
Transactions
on
Graphics, 25(3), July 2006, pp. 826834.
 Steven An, Theodore Kim and Doug L. James, Optimizing Cubature for Efficient
Integration of Subspace Deformations, ACM Transactions on
Graphics (SIGGRAPH ASIA Conference Proceedings), 27(5), December 2008,
pp. 165:1165:10.
 Theodore Kim and Doug L. James, Skipping Steps in Deformable Simulation
with Online Model Reduction, ACM Transactions on Graphics
(SIGGRAPH ASIA Conference Proceedings), 28(5), December 2009, pp.
123:1123:9.
 Jeffrey Chadwick, Steven An, and Doug L. James, Harmonic Shells: A Practical Nonlinear
Sound Model for NearRigid Thin Shells, ACM Transactions on
Graphics (SIGGRAPH ASIA Conference Proceedings), 28(5), December 2009,
pp. 119:1119:10.

Wed20Apr

Discussion
(Ian
Lenz)

Ozden,
K.E.;
Schindler,
K.;
Van
Gool, L.; Multibody
StructurefromMotion
in
Practice, Pattern Analysis and
Machine Intelligence, IEEE Transactions on, vol.32, no.6,
pp.11341141, June 2010.

Mon25Apr

PhysicsBased
Sound
Rendering

Topics
Discussed:
 Sound rendering problems
 Acoustic radiation problems
 Sound waves
 Derivation of wave equation
 Approximation
 Application to solids and fluids
 Case study: Harmonic Fluids
References:
 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.
 Kees van den Doel, Paul G. Kry, Dinesh K. Pai, FoleyAutomatic: PhysicallyBased Sound
Effects for Interactive Simulation and Animation,
Proceedings of
ACM SIGGRAPH 2001, Computer Graphics Proceedings, Annual Conference
Series, August 2001, pp. 537544. [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. 8796. [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. 529536.
 Perry R. Cook, Sound
Production and Modeling, IEEE Computer Graphics &
Applications, 22(4), JulyAugust 2002, pp. 2327.
 Yoshinori Dobashi, Tsuyoshi Yamamoto, Tomoyuki Nishita, RealTime Rendering of Aerodynamic Sound
Using Sound Textures Based on Computational Fluid Dynamics,
ACM Transactions on Graphics, 22(3), July 2003, pp. 732740. [project
page]
 Doug L. James, Jernej Barbić and Dinesh K. Pai, Precomputed Acoustic Transfer:
Outputsensitive, accurate sound generation for geometrically complex
vibration sources, ACM Transactions on Graphics, 25(3), pp.
987995, July 2006, pp. 987995.
 Changxi Zheng and Doug L. James, Harmonic Fluids, ACM Transaction
on
Graphics (SIGGRAPH 2009), 28(3), August 2009, pp. 37:137:12.
 Jeffrey Chadwick, Steven An, and Doug L. James, Harmonic Shells: A Practical Nonlinear
Sound Model for NearRigid Thin Shells, ACM Transactions on
Graphics (SIGGRAPH ASIA Conference Proceedings), 28(5), December 2009,
pp. 119:1119:10.
 Changxi Zheng and Doug L. James, RigidBody Fracture Sound with Precomputed
Soundbanks, ACM Transactions on Graphics (SIGGRAPH 2010),
29(3),
July 2010, pp. 69:169:13.
 Changxi Zheng and Doug L. James, Toward HighQuality Modal Contact Sound,
SIGGRAPH
2011
(to
appear)

Mon25Apr 
Discussion (Albert Liu)

Huamin Wang, Gavin
Miller and Greg Turk.
2007.
"Solving General Shallow Wave Equations on Surfaces". In Proceedings
of
ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA) 2007,
pp. 229  238, San Diego, USA. [PDF
2.3MB], [AVI
in
DivX 46MB] [BibTex]

Wed27Apr

Computational
Motion
Project Presentations (Part I)

Presentations:
 Kevin & Ivo
 Greg & Nathan
 Albert
 Chuck & Mark
 Himanshu & Jonathan

Mon2May

Computational
Motion
Project Presentations (Part II)

Presentations:
 Jeff
 Andy
 Ian
 Yunfeng
 Jiexun

Wed4May

No
class


Wed18May
Due Date

Complete
Projects
&
Reports

Submit
(via
CMS)
by
Wed
May
18.


End of classes!

