CS 448 - Topics in Computer Graphics

Mathematical Methods for Computer Graphics

Pat Hanrahan, Eric Veach, and Denis Zorin

Autumn, 1997
3 (+/NC or letter grade)
limited to 25 students
Time and Place
Tue/Thu 2:30 - 3:45, 392 Gates Hall (graphics lab conference room)
Pat Hanrahan, Eric Veach, and Denis Zorin
Teaching Assistant
Cindy Chen
Office hours
Home Page
CS 348A - Computer Graphics: Mathematical Foundations
CS 348B - Computer Graphics: Image Synthesis Techniques

Course Abstract

Recent work in computer graphics has been stimulated by a variety of mathematical techniques, both classical and new. The goal of this course is to introduce students to some of these mathematical concepts, to show how they are useful in computer graphics, and to provide a starting point for graduate students who wish to apply these ideas in their own research. We will cover the following topics: wavelets, subdivision surfaces, Monte Carlo algorithms, interval techniques and automatic differentiation, and differential geometry.


Three will be 4 written assignments, corresponding to the major topics of the class: In addition, each student will be required to submit typeset notes of one lecture, and proof-read notes for another. The assignments will mostly consist of mathematical problems, little if any programming will be required.

Grading Policies

There will be no exams. The grade will be based on assignments. Each assignment will count as 25% of the grade; no one can pass the class without submitting satisfactory notes for the assigned lecture and ALL assignments.

Late Assignments If you expect that you won't be able to turn in the assignment on time, notify us in advance to avoid late penalties. Unexpected circumstances will be considered on individual basis. The penalty is 5% a day; the assignments cannot be turned in more then one week after the deadline.

Collaboration You may discuss the problems with friends, but we recommend that you think about the problem yourself before discussing it with anyone. You should not read complete solutions written by other people.

Textbooks and Reading

There will be no textbooks required for the class. We will provide you with lists of recommended books for each topic. The primary source of information at the class will be the lectures. We will try to provide you with copies of our slides or notes for the lectures. In addition, we will make copies of journal articles and papers on the topics covered in the class. The problems in the assignments may rely on the material which is not presented in class but is discussed in the handouts.


We ask each person in the class to scribe one lecture and review the notes produced by another student for a second lecture. The collection of these notes will be made available to all students in the class. A significant part of the material presented in the class is not covered or is not presented in a concise form in any textbook, and a collective effort would allow us to create a set of notes that no student or lecturer would be able to put together on his own. In addition, scribing one of the lectures would definitely give you an opportunity to understand a topic in greater detail.

The scribing assignments will be made after the first class meeting. The notes should be typeset and reviewed within one week after the lecture; the version including corrections suggested by the reviewer is returned to the lecturer for final review; the lecturer might request further changes in the notes. The final version of the notes will be made available to the class.

There are also some additional scribing resources available.

Last update: September 24, 1997

Copyright © 1997 Pat Hanrahan, Eric Veach, and Denis Zorin