Fundamentals of Computer Animation
COMP 559 - Winter 2011

General Information

Web Page
Lectures 4:05 PM - 5:25 PM, Mondays and Wednesdays
Location MC 103
Credits 4
Instructor Paul Kry
Telephone 514 398 2577
Office MC113N
Office Hours 2 pm Tuesdays, or by appointment (any time!)
Teaching Assistant Olivier Rémillard,
TA Office Hours MC 312, Thursdays, 12:30-1:30

Overview and Objectives

This course will provide an introduction to computational techniques for generating animation. Topics will include methods which have applications in the creation of movie effects, the development of video games, and training simulations. While the focus will largely be on physically based methods for the automatic generation of motion, approximately half the course will cover methods for user control of animation and reuse of captured motion data. See the schedule below for a list of topics.

The main objective of this course is to have students develop an understanding of fundamental techniques used for computer animation. At the end of the term, students will be able to identify the advantages and disadvantages of using simulation, procedural animation, motion capture, and hand designed animations, with respect to both online and offline applications. You will also be able to implement animation techniques, using common software languages and tools. Finally, in addition to an understanding of current practices in computer animation, a general objective is for students to better recognize current important challenges in computer animation.


Undergraduate students taking this course should have already taken COMP 557 (Fundamentals of Computer Graphics) and COMP 350 (Numerical Computing), or in special cases ask for consent of the instructor. Students taking this course should have good knowledge of linear algebra, calculus, and be comfortable programming in Java for assignments.

Course format and evaluation

The class will be taught through a series of lectures. Grading will be largely based on assignments and a project as the intent is for students to get hands on experience with the material in the course. There are four components to the grading scheme.

  • 40% assignments (4 programming assignments)
  • 10% written questions (assigned with assignments or in alternate weeks)
  • 20% midterm exams (two in class tests)
  • 30% project (write up, presentation, and oral)


Assignments must be all your own work. You are still encouraged to discuss material related to the assignments with your classmates, that is, discuss your assignments, problems, or solutions as a group, but you are ultimately responsible for understanding the material and the programming and write up must be all your own work. If you do talk with your classmates about the assignment, then you must list the names of everyone with which you discussed the assignment, or state that you discussed with nobody.

See below the section on things you should already know about academic integrity. Also note that you can submit work in French if you prefer. If ever you feel you can't complete the work, talk to me, or your advisor, and we can help you figure out what to do (i.e., don't wait until the end of the term).

Programming assignments must be submitted electronically (follow the instructions in the assignment specification). Assignments will typically be due at noon. Late assignments will be accepted up to three days after the deadline and will receive a penalty of 10%.

You should always check your submission by downloading your assignment from the server and checking that it is what you intended to submit. The written component of an assignment, if any, must be submitted as a PDF (i.e., a clear scan, or photo, or use latex or some other typesetting software).

Here follows the list of tentative assignments. Note that there will only be 4 assignments and for each you will have approximately two weeks to complete the objectives (you will have more than two weeks for the project).

Texts and Resources

Material in this course will come from a number of sources. All suggested and supplementary texts will be on reserve at the Schulich library. The CAAT book is highly recommended for students wanting an general resource and slightly gentler introduction to the material, while the PBA book is suggested as a good supplementary resource on the Physics-Based Animation topics. The course will also make use of a number of excellent free online resources (PBM, MLS), and additional notes on selected materials will be provided through out the term.

Schedule (Tentative)

1 jan 5 Introduction
2 jan 10 Physics-based animation with ODEs, second order motion, springs, dampers, gravity
3 jan12 Implicit and explicit methods, solving sparse systems
4 jan 17 Numerical vs exact solutions
5 jan 19 Numerical solutions to ODEs, and absolute stability
6 jan 24 Rigid body motion in 2D a1 due
7 jan 26 Collision detection, BVs and hierarchies
8 jan 31 Collision response, penalty forces and contact constraints
9 feb 2 Constraints, energy formulation, Lagrange multipliers
10 feb 7 Linear complementarity problem
11 feb 9 Motion capture tech, capture reuse challenges a2 due
12 feb 14 Control for character animation, ODE library
13 feb 16 Midterm (in class)
reading week
14 feb 28 Eulerian fluid simulation a3 due
15 mar 2 Eulerian fluid simulation review, and survey of alternative methods
16 mar 7 Constraint stabilization, Baumgarte, manifold projection, post step
17 mar 9 Rigid body motion, exponential map and Rodrigues' formula
18 mar 14 Rigid body motion, logarithmic map a4 due
19 mar 16 Rigid body motion, rotational relative veloctiy
20 mar 21 Rigid body motion, adjoint transformation
21 mar 23 Rigid body equations of motion
22 mar 28 forward and inverse kinematics
23 mar 30 FEM, Elastic solids
24 apr 4 Corotational finite elements
25 apr 6 Survey of other animation techniques (skinning, keyframe, spacetime optimization)
26 apr 8 Midterm (in class)
TBA Final presentations

In case you didn't already know...

McGill University values academic integrity. Therefore, all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures. See for more information, as well as, the Student Guide to Avoid Plagiarism.

It should be noted that, in accordance with article 15 of the Charter of Students' Rights, students may submit examination answers in either French or English.

According to Senate regulations, instructors are not permitted to make special arrangements for final exams. Please consult the Calendar, section, General University Information and Regulations at Special arrangements in emergencies may be requested at your Student Affairs Office. If you have a disability, please advise the Office for Students with Disabilities (398-6009) as early in the term as possible so that we can provide appropriate accommodation to support your success.

In the event of circumstances beyond the instructor's control, the evaluation scheme as set out in this document might require change. In such a case, every effort will be made to obtain consensus agreement from the class.

Additional policies governing academic issues which affect students can be found in the Handbook on Student Rights and Responsibilities, Charter of Students' Rights.