Topics in Computer Graphics

Monday 1:15 pm-3:15 pm

719 Broadway, room 1221.

Denis Zorin, office hours: Tuesday 1-3 pm and by appointment


This course discusses the basics and state of the art of physically-based modeling for computer graphics and related fields. The topics covered will include a review of the necessary background in mechanics, relevant numerical methods and discussions of recent research papers in the area. The focus will be on simulation of dynamics of rigid and deformable objects.


Mathematics: linear algebra, basic numerical methods, mechanics.
Computer Science: solid programming ability in at least one language (preferably C++).


Project. The grade will be primarily based on the course project. A list of suggested projects will be provided; however, students may choose their own project. Group projects are encouraged. In either case, the intended project should be discussed with the instructor.
Assignments. There will be one or two assignments.
Paper presentation. Each student is required to present one or more papers (depending on the number of students in the class). Presentations should be 30 min. long + 10 min for questions and discussion. The presenter should prepare slides for the presentation, which should be sent to the instructor for review no later than Friday before the presentation.
Scribing. Each student will be expected to be a scribe for a lecture. Scribes are expected to take detailed notes and produce a typeset version of the notes to be distributed to the class. Detailed instructions for notes and LaTeX templates are here

Reading materials

The course will be based on a collection of papers and notes. Links to relevant materials on the Web will be added to the list of lectures below.


September 22 Last date to drop or add the class.

October 6 Choice of project.

October 13 Project proposal.

December 8 Project presentations.

Project Suggestions


September 8 Overview. Review: basic ordinary differential equations; particle dynamics.
Reading: Witkin and Baraff's notes.
September 15Rigid body mechanics.
September 22Constraints. Handling constraints numerically.
September 29Fast rigid body simulation in graphics.
D. Baraff. Fast contact force computation for nonpenetrating rigid bodies. Presenter: Ilya Rosenberg.
D. Baraff. Linear-time dynamics using Lagrange multipliers. Presenter: Elif Tosun.
B. Mirtich. Timewarp Rigid Body Simulation. Presenter: Yotam Gingold.
October 6 Handling collisions in simulation.
Guendelman, E. et al. Nonconvex rigid bodies with stacking. Presenter: Matthew Grimes.
October 13 Spacetime constraints. Control of rigid body simulations.
Jovan Popovic et al. Interactive Manipulation of Rigid Body Simulations. Presenter: Raul Sierra.
October 20 Elasticity, deformable objects.
Lecture notes. (Adrian Secord, Yotam Gingold).
October 27 Finite element method, 2D and 3D elements.
November 3 Deformable object simulation in graphics.
D. Terzopoulos et al. Elastically deformable models. Presenter: Jonathan Lippincott.
D. James and D. Pai. ArtDefo: Accurate Real Time Deformable Objects. Presenter: Du Nguyen.
November 10 Guest lecture. O'Brien et al. Graphical Modeling and Animation of Brittle Fracture. Presenter: Adrian Secord.
November 17 Guest lecture.
November 24 Anatomically-based modeling of humans. and animals.
Irene Albrecht. et al Construction and Animation of Anatomically Based Human Hand Models.
J. Wu. Realistic Modeling of Bird Flight Animations Presenter: Kristofer Schlachter.
December 1 Cloth simulation.
SIGGRAPH cloth animation course notes.
K.-J. Choi, H.-S. Ko. Stable but Responsive Cloth. Presenter: Sung Hee Lee.
December 8 Overview of fluids in computer graphics: stable fluid simulation, free surface simulation.
J. Stam. Stable Fluids.
D. Enright et al. Animation and Rendering of Complex Water Surfaces. Presenter: Harper Langston.
December 15 Project presentations.

Denis Zorin