Geometry for Computer Graphics
Math 431 Fall 2009


Official Course Number: MATH 431 (Section 0101) (3 credits)
Grade Method: REG/P-F/AUD.
Lectures: Tuesday-Thursday 11:00 - 12:15, 0103 Math Building
Professor: Bill Goldman (wmg@math.umd.edu)
Office: 3106 Math Building
Phone: 301-405-5124
Office hours: Tuesday/Thursday 1:00- 1:45 or by appointment.

Prerequisites: MATH240 or MATH461

This course explores the use of geometry (including projective geometry) in computer graphics. Click here for a brief description/advertisement. The course is structured around problem set handouts (to be discussed in the lecture and eventually collected) and four in-class exams.

Text: Applied Geometry for Computer Graphics and CAD, Second Edition, by Duncan Marsh, Springer Undergraduate Mathematics Series, ISBN 2-85433-801-6 (1999,2005)

Tentative Syllabus:

  1. Transformations, translations, affine spaces (9/1, 9/3)
    Affine spaces and translations (second lecture, 9/3)
  2. Transformations of the plane (9/8, 9/10)
  3. Plane geometry via complex numbers
  4. The closest point on a line
  5. Shears and nilpotent matrices (10/1)
  6. Introduction to Projective Geometry: homogeneous coordinates
  7. Coordinate transformations, quaternions, Plucker coordinates
  8. Bezier Curves, Splines

  • First problem set: 1.1, 1.4, 1.7, 1.8, 1.10, 1.13, 1.16, due Thursday 9/10
  • The first worksheet was distributed Tuesday, September 15. The exercises are due Tuesday, September 22.
  • The first test was given Tuesday, September 22.
  • The second problem set was given Thursday, October 1 (and due Thursday, October 15):
    • 2.3, 2.4, 2.8, 2.9, 2.14, 2.15, 2.16, 2.18, 2.21, 2.23, 2.27 2.29
  • The second test was given Tuesday, October 13.
  • The third problem set was given Thursday, October 15 (and due Thursday, October 22): All problems (3.1-3.11) in Chapter 3 before the section on quaternions.

History of Math 431:
The course was last taught in Fall 2008. and, before that, in Fall 2006.. Click here for some of the class projects from 2006.

Emeritus Professor Garry Helzer developed Math 431, using Mathematica software. Click here to see his course notes. They are in the form of Mathematica notebooks. My approach is somewhat different, as a look at the web pages will indicate.

Andrejs Treiberg's course The Geometry of Perspective Drawing on the Computer looks particularly relevant and accessible.

Makeups:
There will be no makeups for quizzes or midterms. If illness, a death in the family, car trouble or a faulty alarm clock cause you to miss a midterm -- that is the midterm or section quiz you will drop. So do not decide an earlier midterm or quiz is going to be your bad score -- if you miss a later one, then that is going to be your bad score. When you have compelling reasons for missing an exam, share them with me or your TA.
**If you know BEFORE an exam that you have a conflict, contact me in advance. In this case, it is sometimes possible to arrange an early exam.**

Deadlines:
Deadlines. Late homework will not be accepted. Here are two reasons: we want to use resources well (it is much more time consuming to grade homework when it is late), and you will learn better if you do the work on time.

Emergency closures:
In case of an emergency that closes the University for an extended period of time (for example, due to inclement weather), be sure to access your email for instructions from me. Also check the University's home page.

Expectations/philosophy:
You are expected to come to class, do the homework, and most important of all be actively engaged in trying to understand. Two tips for success: Don't fall behind. Make friends. Help each other (especially after trying alone first).

Religious observances:
If your religion dictates that you cannot take an exam or hand in assigned work on a particular date, then contact me at the beginning of the semester to discuss alternatives. You are responsible for making these arrangements at the beginning of the semester.

Disabilities:
If you have some disability related to testing under the usual timed, in-class conditions, you may contact the office of Disabled Students Services (DSS) in Shoemaker. If they assess you as meriting private conditions and/or extra time, then you may arrange to take your tests at DSS, with extra time as they indicate. You must arrange this well in advance of a test (in particular: no retakes). Click to Disability Support Services for further information.

Course Evaluations:
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wmg@math.umd.edu

Last modified: 19 October 2009