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., Har-Peled, 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), 550-572.
|
MonJan31
WedFeb2
|
Euler-Lagrange
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:
- N-body problems (all-pairs complexity)
- Reduced-coordinate 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 N-body planar serial manipulator
from class: Given joint
angles and
velocities, what is the
complexity of naive evaluation of joint
accelerations from the expanded Euler-Lagrange 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_j-p_k)
- distances, ||p_j-p_k||
- distance powers, ||p_j-p_k||^n
- dot products, (p_1-p_0)^T (p_3-p_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, 43-54.
- 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
- Rigid-body 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
- Newton-Euler equations of motion
- Integrating rigid-body 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
Rigid-Body 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 Newton-Euler Algorithm (RNEA)
- Composite-Rigid-Body Algorithm (CRBA)
- Usage in O(N^3) forward dynamics (CRBA + RNEA + dense
solve)
- Articulated-Body Algorithm (ABA)
- a.k.a. "Featherstone's algorithm"
- O(N) forward dynamics
- Closed-loop 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 book--highly readable)
- Roy Featherstone, A Divide-and-Conquer Articulated-Body
Algorithm for Parallel O(log(n)) Calculation of Rigid-Body Dynamics.
Part 1: Basic Algorithm, The International Journal of
Robotics Research, Vol. 18, No. 9, 867-875, 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, Linear-Time Dynamics using
Lagrange Multipliers, Proceedings of
SIGGRAPH 96, Computer Graphics
Proceedings, Annual Conference Series, August
1996, pp. 137-146.
- Robot
dynamics, Scholarpedia page.
- D.K. Pai, STRANDS: Interactive Simulation of Thin
Solids using Cosserat Models, Computer Graphics Forum,
21(3), pp. 347-352, 2002.
|
MonFeb21
|
Discussion:
Articulated Body Algorithm (ABA)
|
Reference:
|
MonFeb21
|
Constrained
Dynamics
and
Differential-Algebraic
Equations
(DAEs)
|
References
for
Differential-Algebraic
Equations
(DAEs):
Topics discussed:
- Constrained Lagrangian dynamics
(CLD)
- Holonomic constraints
- Constraint-augmented Lagrangian
- Examples, e.g., pendulum
- DAE systems
- Differentiation index
- Structure of index-1, -2, and -3 DAE systems
- Index reduction by differentiation
- Drift-off phenomena
|
WedFeb23
|
Integrating
Constrained Dynamics
|
Topics
discussed:
- Constrained Lagrangian dynamics in index-1, -2, -3 and GGL
DAE forms
- Solving for Lagrange multiplier from index-1 form.
- Constraint stabilization:
- Baumgarte's method; modified Lagrange multiplier
- Projection (position, velocity)
- Implicit integration of DAEs (for stiff problems)
- General DAEs, and semi-explicit index-1 DAEs
- Backwards Euler
- BDF and multistep methods
- Half-explicit Runge-Kutta 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
- Velocity-level contact formulation
- The myth of "contact points"; distributed friction
forces;
planar sliding; center of friction
- Contacting multibody systems
- Nonpenetration constraints; Signorini-Fichera
condition
- Maximal dissipation principle
- "Staggered Projections" contact algorithm
- Iterative solvers; projected Gauss-Seidel methods
References:
- D.E. Stewart, Rigid-Body Dynamics with Friction and Impact,
SIAM
Review,
42(1),
pp.
3-39,
2000.
- D. Baraff, Fast contact force computation for
nonpenetrating rigid bodies, Computer Graphics Proceedings,
Annual Conference Series: 23-34, 1994. (cover's Dantzig's algorithm)
- D. Baraff, Coping with
friction for non-penetrating rigid body simulation, Computer
Graphics 25(4): 31-40, 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, Impulse-based 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 velocity-level
iterative contact solver)
- Kenny Erleben, Velocity-based shock
propagation for multibody dynamics animation, ACM Transactions on Graphics, 26(2), June 2007, pp. 12:1-12:20. (good summary of a velocity-level
projected Gauss-Seidel contact solver)
- Christopher D. Twigg, Doug L. James, Backward Steps in Rigid Body Simulation, ACM Transactions on Graphics, 27(3), August 2008, pp. 25:1-25:10.
(see for summary of
velocity-level 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
- Navier-Stokes equation
- MAC grid discretization; interpolation and
averaging; upwinding
- Time-stepping schemes (Eulerian, and semi-Lagrangian)
- Projection to divergence-free velocity
- Poisson equation; discretization; compatibility
condition; PCG solution
- DAE view of incompressible flow
- Higher-order semi-Lagrangian 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,
Springer-Verlag, 2003.
- U.M. Ascher and L.R. Petzold, Computer
Methods
for
Ordinary
Differential
Equations
and
Differential-Algebraic
Equations, SIAM.
- Jos Stam,
Stable Fluids, Proceedings of
SIGGRAPH 99, Computer Graphics Proceedings, Annual Conference Series,
August 1999, pp. 121-128.
- 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)
- 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]
- Foster, N. and Fedkiw, R., Practical Animation of Liquids,
SIGGRAPH 2001, 15-22 (2001).
- Enright, D., Marschner, S. and Fedkiw, R., Animation and Rendering of Complex Water
Surfaces,
SIGGRAPH 2002, ACM TOG 21, 736-744 (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)
- Higher-order 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 135-144, 2007. video(DivX)
- Selle, A., Fedkiw, R., Kim, B., Liu, Y., and Rossignac,
J. 2008. An Unconditionally Stable MacCormack Method.
J. Sci. Comput. 35, 2-3 (Jun. 2008), 350-371.
- 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.1-10, 2010. [PDF] [Video+Code]
- A
coarse-grid
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,
GPU-based
Real-Time Soft Tissue Deformation with Cutting and Haptic Feedback, Progress in Biophysics and
Molecular Biology 103, 2-3, 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 5-minute presentation
on their project topic, current results/progress, and goals for the
remaining month.
|
Wed6Apr
Mon11Apr
|
Gradient-Domain
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.
399-405.
- Robert W. Sumner, Matthias Zwicker, Craig Gotsman, Jovan
Popović, Mesh-based Inverse Kinematics,
ACM Transactions on Graphics, 24(3), August 2005, pp. 488-495.
|
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. 43-51 |
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. 74:1-74:8.
- Pushkar Joshi, Mark Meyer, Tony DeRose,
Brian Green, Tom Sanocki, Harmonic Coordinates for
Character Articulation, ACM
Transactions on Graphics, 26(3), July 2007, pp. 71:1-71:9.
|
Wed13Apr
Mon18Apr
|
Collision
Detection,
and
Subspace Deformation Bounds
|
Topics
discussed:
- Bounding volumes (spheres, boxes, k-DOPs, etc)
- Separating axis theorem
- Space-time bounds
- Bounding moving points
- Bounding subspace deformations;
- Bounded Deformation Trees
- O(r) and O(1) updates
- Spheres, boxes, k-DOPs
- Translational and affine/rotational models
References:
- Philip M. Hubbard. 1996. Approximating polyhedra with spheres for
time-critical collision detection. ACM Trans. Graph.
15, 3 (July 1996), 179-210. 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. 325-338, 1999.
- Miniball
software, Smallest Enclosing Balls of Points - Fast and Robust in
C++.
- Doug L. James, Dinesh K. Pai, BD-Tree: Output-sensitive collision
detection for reduced deformable models, ACM Transactions on
Graphics, 23(3), August 2004, pp. 393-398. [SIGGRAPH
Talk]
- M. Teschner et al., Collision Detection for Deformable Objects,
Eurographics
State-of-the-Art
Report
(EG-STAR),
Eurographics
Association,
pages
119-139,
2004.
- Jernej Barbič and Doug L. James, Six-DoF 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 6-DOP 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. 23:1-23:9. |
Wed20Apr
|
Subspace
Dynamics;
Physics-Based
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
- Reduced-order deformation force models
- exact reductions (linear, StVK)
- approximations (cubature)
- Reduced-order 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, 253-279, 1985.
- A. A. Shabana, Theory of
Vibration (Volume II: Discrete and Continuous Systems),
Springer-Verlag, New York, NY, 1990.
- P. Krysl, S. Lall, and J.E. Marsden, Dimensional
model
reduction
in
non-linear finite element dynamics of solids and
structures, Int. J. for Numerical Methods in Engineering, 51,
479-504, 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. 582-585.
- Jernej Barbič and Doug L. James, Real-Time Subspace Integration of
St.Venant-Kirchhoff Deformable Models, ACM Transactions on
Graphics (ACM SIGGRAPH 2005), 24(3), pp. 982-990, August 2005, pp.
982-990.
- Adrien Treuille, Andrew Lewis, Zoran Popović, Model reduction for real-time fluids,
ACM
Transactions
on
Graphics, 25(3), July 2006, pp. 826-834.
- 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. 165:1-165:10.
- 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.
123:1-123:9.
- 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.
|
Wed20Apr
|
Discussion
(Ian
Lenz)
|
Ozden,
K.E.;
Schindler,
K.;
Van
Gool, L.; Multibody
Structure-from-Motion
in
Practice, Pattern Analysis and
Machine Intelligence, IEEE Transactions on, vol.32, no.6,
pp.1134-1141, June 2010.
|
Mon25Apr
|
Physics-Based
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. 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.
- 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.
- Changxi Zheng and Doug L. James, Toward High-Quality 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!
|
|