CS 6650: Computational Motion (Spring 2011)

Professor:     Doug James
                      5146 Upson Hall
                      Office Hours: after class, or by appointment
                      djames 'at' cs.cornell.edu

Logistics:      Mon/Wed @ 2:55--4:10pm  in  (Room Change: Thurston 205)
                      First Class:  Wednesday, Jan 26  (please attend for more information)

Course Description: Covers computational aspects of motion, broadly construed. Topics include the computer representation, modeling, analysis, and simulation of motion, and its relationship to various areas, including computational geometry, mesh generation, physical simulation, computer animation, robotics, biology, computer vision, acoustics, and spatio-temporal databases. Students implement several of the algorithms covered in the course and complete a final project.  This Spring 2011 offering will also explore the special role of motion processing in physically based sound rendering.

Prerequisites: Undergraduate-level understanding of algorithms, and some scientific computing.

Grade options: Letter or S/U

Credit hours: 4

Offered: Fall only

Cross-Listing: None

Grading Rubric:
    30%   Paper presentations, and submitted questions.
    30%   Written homeworks
    05%   Project: Written proposal
    05%   Project: Mid-course show-and-tell
    05%   Project: Final public presentation
    25%   Project: Final written report

Discussion Group: http://groups.google.com/group/cornellcs6650spring2011  (restricted access to students in course)

Class Schedule: (link to fall 2008 schedule)

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:
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:

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)
    • O(N) inverse dynamics
  • Composite-Rigid-Body Algorithm (CRBA)
    • O(n^2)  mass matrix 
    • 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:
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:
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)
[Parker et al. 2009]
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:
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 et al. 2010]
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:
Wed6Apr
Discussion (Jiexun Xu)
Time stepping through functional minimization
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)
http://graphics.pixar.com/library/SoftCachingB/thumbNail.png
References:
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:
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)
http://graphics.stanford.edu/projects/lgl/papers/mknpga-pbaepmo-04/image.gif
M. Müller, R. Keiser, A. Nealen, M. Pauly, M. Gross, M. Alexa, Point Based Animation of Elastic, Plastic and Melting Objects, SCA 2004.
http://graphics.ethz.ch/disclaimer.php?dlurl=/Downloads/Publications/Papers/2004/Mue04c/Mue04c.pdf

Videos:
http://graphics.ethz.ch/Downloads/Publications/PaperVideos/2004/Mue04c%20Matthias_Mueller%20-%20PBA_Elatsic_Plastic_Melting%20-%20SCA04.avi
http://graphics.ethz.ch/Downloads/Publications/PaperVideos/2004/Mue04c%20Matthias_Mueller%20-%20PBA_Elatsic_Plastic_Melting2%20-%20SCA04.avi
Mon18Apr
Discussion (Nathan Lloyd & Greg Sadowski)
[Ozgen et al. 2010]
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:
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:
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!