CS 5643: Physically Based Animation for Computer Graphics
Spring 2014


PROFESSOR:  Doug James

TA: Eston Schweickart

HELP SESSIONS AND OFFICE HOURS: 
After class, and by appointment. Please also ask questions on the Piazza forum.

DESCRIPTION:  Modern computer animation and interactive digital entertainment are making increasingly sophisticated use of tools from scientific and engineering computing. This course introduces students to common physically based modeling techniques for animation of virtual characters, fluids and gases, rigid and deformable solids, and other systems. Aspects of interactive simulation and multi-sensory feedback will also be discussed.  A hands-on programming approach will be taken, with an emphasis on small interactive computer programs.

TIME:  TR 2:55-4:10pm

LOCATION:  Gates G01 (new location!)

   
SCHEDULE (Previous Spring 2013 Link)
DATE
TOPICS
SUPPLEMENTAL MATERIALS
ThJan23 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, 191-209. 
TuJan28 Particle Systems
Material:
ThJan30
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 half-explicit) DAE integration schemes)
  • Post-step projection schemes
    • Position- vs velocity-based corrections
  • Applications: Mechanical linkages, inextensibility constraints, incompressible flow, contact constraints
References:
[Advanced] References for Differential-Algebraic Equations (DAEs):
TuFeb04
Particle-based Fluids



Material:
ThFeb06
No Class
Prof. James is away at NYU.

Read: ([Müller et al. 2003], SPH course notes), and Position Based Fluids.
TuFeb11
Particle-based Fluids (cont'd)

ThFeb13 Assignment #1:
Position Based Fluids
Project webpage. Starter code is on CMS.
TuFeb18
Winter Break
No class
ThFeb20
Basic Integrators

Material:
  • Forward Euler
  • Backward Euler
  • Symplectic Euler (a.k.a. semi-implicit Euler); symplectic Euler adjoint
    • E. Hairer, C. Lubich, and G. Wanner. Geometric Numerical Integration. Structure-Preserving Algorithms for Ordinary Differential Equations., Springer Series in Comput. Mathematics, Springer-Verlag, volume 31, 2002.
  • Midpoint method
  • Verlet method (a.k.a. Störmer's method)
  • Stability analysis of forward & backward Euler schemes on test problem

Implicit Integration;
IMEX and other schemes

Material:
TuFeb25
Review: Tensor Calculus

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
  • functions of distance, W(||p_j-p_k||)
  • dot products, (p_1-p_0)^T (p_3-p_2)
  • cross products
  • Example: hair bending energy derivative, E = k*sin^2(theta/2)  [handout]
Other topics:
ThFeb27
TuMar04
Position Based Dynamics

References:
ThMar06
Assignment #2:
Position Based Dynamics

Project webpage. Starter code on CMS.
ThMar06
TuMar11
ThMar13
Robust Collision Processing
Material:
  • Motivation: cloth and hair animation
  • Continuous collision detection
    • 2D/3D sphere-sphere, 2D (point-edge), and 3D (point-face, edge-edge) tests
  • Velocity-level collision resolution; collision impulses
  • Supporting pin/trajectory constraints
    • Inverse-mass-matrix filtering
  • Penalty forces
  • Rigid cloth zones
References:
TuMar18
Rigid Body Simulation
Material:
  • Rigid body dynamics
    • Position, orientation, linear/angular velocity, momentum, inertia, equations of motion, etc.
    • Euler's equations of angular rigid-body dynamics (in body coordinates)
  • Contact impulses
  • Example: "rigid damping"
  • Frictionless contacts:
    • Nonpenetration constraints
    • Velocity-level constraints (see Baraff course notes for acceleration-level constraints)
    • Linear Complementarity Problem (LCP)
References:
ThMar20
No class
SIGGRAPH PC Meeting
TuMar25
Proposal for Final Project Webpage
  • Project proposal (PDF format) [DUE: Thursday April 10]
TuMar25
ThMar27
TuApr08
Rigid Body Contact:
Impulse- and Constraint-based Methods


Material:
TuApr08
ThApr10
Passive Rigid Motion Control



Material:
  • Simulation accuracy vs plausibility
  • Exploiting errors for control
    • Random sampling methods
    • Optimization based methods
    • Interactive artist-driven methods
References:
TuApr15
ThApr17
Fluid Animation
Materials:
ThApr17
The Conjugate Gradient Method
Material:
  • Jonathan Richard Shewchuk, An Introduction to the Conjugate Gradient Method Without the Agonizing Pain, August 1994.  PDF (516k, 58 pages)
  • G.H. Golub and C.F. Van Loan, Matrix Computations, 4th Edition, Johns Hopkins University Press, 2013.
TuApr22
Fracture Animation

Material:

ThApr24
Animation Sound





Material:
TuApr29
Yarn-level Cloth Simulation
(Guest lecturer: Eston Schweickart)


ThMay01
Project working session
(Prof. James at SIG CHI)
TuMay06
Project Presentations

Tentatively organized for an extended in-class presentation period. The CS colloquium no longer meets after our class, and therefore we can extend the class into the following slot and remain in Gates G01.









SUPPLEMENTAL MATERIAL

TOPICS
SUPPLEMENTAL MATERIALS
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:

From Spring 2013:

Assignment #1
Particle Systems


  Assignment #1 Homepage


Assignment #2
Robust Collision Processing
(a.k.a. "The Spaghetti Factory")
Assignment #2 Homepage
  • Video highlights (from previous years):

Solving Sparse Linear Systems

Material:

Assignment #3
Rigid Body Contact
(a.k.a. "The Jelly Bean Factory")
Material:
  • Starter code available from CMS 

Smoke Control
Materials:

Fluid-Solid Coupling
Materials:

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. 471-478. [ACM] [PDF] [AVI]
  • Alec R. Rivers, Doug L. James, FastLSM: Fast Lattice Shape Matching for Robust Real-Time Deformation, ACM Transactions on Graphics, 26(3), July 2007, pp. 82:1-82:6. [ACM] [PDF]
  • Denis Steinemann, Miguel A. Otaduy, Markus Gross, Fast Adaptive Shape Matching Deformations, ACM SIGGRAPH/Eurographics Symposium on Computer Animation, Dublin, July 7-9, 2008. [PDF] [AVI]
  • Matthias Müller and Nuttapong Chentanez. Solid simulation with oriented particles. ACM Trans. Graph. 30, 4, Article 92 (July 2011), 10 pages, 2011. [PDF] [MOVIE]