COMS W4167 Computer Animation

Fall 2017, Columbia University

TR 2:40pm-3:55PM, 417 Mathematics Building

Instructor: Changxi Zheng

Important! We are in the process of setting up Codio to handle programminga assignment submission. So every student will have the same programming environment to work with. We are also going to release start codes and solution executables on the Codio. More details will come soon.

Pre-requisites: Conformable on programming in C++, Data structures (tree, queue, etc.), Multivariable calculus (partial derivative, gradient, Jacobian), Linear algebra (vector, matrix)


Yichen (Peter) Chen (Ph.D. TA,
Chang Xiao (Ph.D. TA,

Office Hours

(Tentative) Schedule

date topic reading assignments
5Sep Introduction (slides)    
7Sep Kinematics    
12Sep Time integration: Symplectic Euler   T1M1 released
14Sep Forces    
19Sep Time integration: Implicit Euler   T1M2 released
21Sep Time integration: Implicit Euler    
26Sep Time integration: Implicit Euler   T1M3 released
28Sep Collision detection & response    
3Oct "Electron clouds   T2M1 released
5Oct Continuous collision detection    
10Oct Broad phase collision detection   T2M2 released
12Oct Broad phase collision detection    
17Oct Broad phase collision detection   T2M3 released
19Oct Constrained mechanical systems    
24Oct Rigid body kinematics   T3M1 released
26Oct Rigid body kinematics Baraff and Witkin's SIGGRAPH course notes  
31Oct Rigid body collisions Numerical methods for linear complementarity problems  
2Nov Elasticity   T4M1 released
7Nov --- University Holiday ---    
9Nov Elasticity    
14Nov Control: Overview   T5M1 released
16Nov Control: discussion of robot assignment    
21Nov Fluids: advection and total derivative   T6M1 released
23Nov --- University Holiday ---    
28Nov Fluids: divergence free vector fields   T6M2 released
30Nov Fluids: free surfaces    
5Dec Advanced topic I   T7 (final project) released
7Dec Advanced topic II    

Projects and Work Load

Throughout this semester, you will have weekly programming assignments organized in a series of themes (see below). For each assignment, we will provide starter code in C++. For the final project, you will propose a project which involves computer graphics techniques that you learn in this class. All projects should be submitted electronically to courseworks. More details will be announced shortly.

Milestone 1 has been released. Deadline: Sep. 18th, 10:00PM.



There will be no exam in this course. But there will be weekly program assignments.


There is no required textbook. In case you need to refresh your Calculus and Linear Algebra background, here are some reference books:

We don't expect you to know OpenGL; our starter code handles all the OpenGL rendering of objects for you. So you won't learn OpenGL in this class. If you want to create your own scences with advanced OpenGL features, here are some references:

About COMS W4167

Grading: We strive to maintain a fast, transparent and fair grading process:

Your final numerical grade will be an average of the numerical grades of all themes. The numerical grade of a theme will be an average of the numerical grades of all milestones in that theme.

Due dates: Weekly deadlines are due on the date and time indicated in the assignment handout, usually at 10:00PM of the day. They must be submitted electronically, as detailed in the assignment.

Lateness policy: Late submissions lose 1% per six minutes of lateness. For example: a submission that is two hours late is penalized 20%, and a submission that is ten hours late receives no credit. Rationale: Since weekly milestones build on each other, we must ensure that all students begin each week at an equal playing field. By enforcing a strict lateness policy, we will be able to post the solution to each milestone shortly after it is due, thereby enabling students to build on a solid foundation in the following week.
Plan ahead. The only exception to this policy is a documented medical emergency. In order to ensure fair grading, exceptions are not possible for holidays, sport meets, theater appearances, indigestion, etc. Plan ahead.

Curving and Final Grade: This class will *not* be curved down. A student achieving a certain percentage grade has a guaranteed minimum letter grade. We reserve the right to curve all grades uniformly upward (improving your letter grade) subject to our discretion. The minimum grade distribution for this class will be given by evaluating the student's numerical grade, after adjusting for lateness, pardon, and extra credit, following the table

with modifiers (+ and -) left to the instructor's discretion subject to considerations such as relative ranking to other students, quality of submitted code, uniformity of quality across assignments.

Questions, help, discussion: The instructors and TAs are available to answer questions, advise on projects, or just to discuss interesting topics related to the class at office hours and by appointment as needed. For electronic communication we are using Piazza (link also available at the top of this page). Please sign up for the Piazza page. When posting questions, please keep them organized by posting them to specific folders.

You are welcome (encouraged, even) to discuss the homeworks and projects among yourselves in general terms. But when you start writing up the homeworks or implementing the projects, you need to be working alone. In particular, it is never permitted for you to see another student's homework writeup or other's program code, and certainly never tolerated to copy parts of one person's writeup, code, or results into another's, even if the general solution was worked out together.

You're also encouraged to read any published sources—books, articles, public web sites—that help you learn. If you find an idea in one of these sources that becomes part of your solution (or even gives you the whole solution), that's fine, but it is imperative that you explicitly cite the source on your homework or state it in a comment of your code. Otherwise you would be falsely claiming to have invented the idea yourself.

Academic integrity: We expect complete integrity from everyone. We assume the work you hand in is your own, and the results you hand in are generated by your program. You're welcome to read whatever you want to learn what you need to do the work, but we do expect you to build your own implementations of the methods we are studying. If you're ever in doubt, just include a citation in your code or report indicating where some idea came from, whether it be a classmate, a web site, another piece of software, or anything—this always maintains your honesty, whether the source was used in a good way or not. The principle is that an assignment is an academic document, like a journal article. When you turn it in, you are claiming that everything in it is your original idea (or is original to you and your partner, if you're handing in as a pair) unless you cite a source for it. it's never OK for you to see another student's homework writeup or another team's program code, and certainly never OK to copy parts of one person's or team's writeup, code, or results into another's, even if the general solution was worked out together.

Cases that violate the academic integrity include (not exclusively):

School can be stressful, and your coursework and other factors can put you under a lot of pressure, but that is never a reason for dishonesty. If you feel you can't complete the work on your own, come talk to the professor or the TAs, or your advisor, and we can help you figure out what to do. Think before you hand in!

Clear-cut cases of dishonesty will result in failing the course.

For more information see Columbia Engineering's Code of Academic Integrity.

Open Door Policy: We hope the course to run smoothly and enjoyably. Feel free to let us know if you find the course helpful and interesting. Especially, let us know sooner about the reverse. Drop by our office hours, leave us a note, or send us an email.