COMS W4167 Computer Animation

Spring 2024, Columbia University

TR 4:10pm-5:25PM, 451 CSB

Instructor: Changxi Zheng

Important! You will be using Codio for doing and submitting your programminga assignments. In this way, 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 be announced on Courseworks.

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


Honglin Chen (uni: hc3284)
Rundi Wu (uni: rw2799)

(Tentative) Schedule

date topic reading assignments
16Jan Intorduction    
18Jan Review of (basic) Newtonian physics    
23Jan Kinematics    
25Jan Time integration: Symplectic Euler    
30Jan Forces    
1Feb Time integration: Implicit Euler    
6Feb Time integration: Implicit Euler    
8Feb Time integration: Implicit Euler    
13Feb Collision detection & response    
15Feb Particle clouds    
20Feb Continuous collision detection    
22Feb Broad phase collision detection    
27Feb Broad phase collision detection    
29Feb Broad phase collision detection    
5Mar Constrained mechanical systems    
7Mar Rigid body kinematics    
12Mar -----------    
14Mar -----------    
19Mar Rigid body kinematics    
21Mar Rigid body collisions    
26Mar Special lecture: TBD    
28Mar Elasticity    
2Apr Elasticity    
4Apr Animation Control    
9Apr Fluids: advection and total derivative    
11Apr Fluids: divergence free vector fields    
16Apr Fluids: free surfaces    
18Apr Fluids: Other simulation methods    
23Apr Deep learning for computer animation    
25Apr Deep learning for computer animation    

Projects and Work Load

Throughout this semester, you will have weekly programming assignments organized in a series of themes (see below). Each theme will have one or more milestones that you need to reach in your assignment submissions. For each assignment, we will provide starter code in C++. All projects should be submitted electronically to Codio. More details about finishing your assignments on Codio will be provided by CAs.



There will be no midterm exam in this course. There will be a take-home final exam.


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, job interviews, 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 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, engagement in the class.

You are allowed 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.