Computational Aspects of Geometric Design

Computer-aided geometric design applications include fair surface design (aerospace), character development
(computer animation),
design study (architecture), and performance evaluation (nautical engineering).


Geometric modeling underlies applications from computer animation and special effects, to advanced modeling software for industrial design and architecture, to rapid prototyping machines that "print" 3-D objects in plastic, and many others. Geometric models represent the shapes and spatial relationships of the environment that is being studied, permitting a much deeper analysis than would be possible otherwise. How these models are encoded, and how the algorithms that utilize them are designed, comprise the field of computer-aided geometric design (CAGD), which is the subject of this course.

We will discuss a wide variety of techniques for representing and analyzing these models. Our emphasis will be on meshes, parametric curves and surfaces, and subdivision methods, but we will discuss less general approaches as well, particularly in relation to online and gaming applications.

To illustrate the material, we will be using a combination of applets, physical models, short films, and software from the animation and design industries, in addition to the class slides. There will be guest lecturers; in the past we've had professionals from the animation, architecture, and industrial design fields.


Michael Reed          
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office hours:
5-6pm Tuesday, or by appointment
Department of Computer Science
Columbia University
500 W. 120th Street, M.C. 0401
New York, New York 10027


Registrar Information

Course ID: E6998 [sometimes also called COMS6998], section 003

Registrar Call #: 10540

This course is 3 points.


Tuesday, 6:10-8:00pm, location: 834 Mudd Building.


In addition to programming proficiency, the student should have a basic understanding of linear algebra and calculus. Having taken one of the courses offered in robotics, vision or graphics will add to the understanding of the course.

Students without these qualifications, who still wish to participate, should speak to the instructor.


Curves and Surfaces for CAGD, 5th edition, by G. Farin, Morgan Kaufmann Publishers, 2002.

Additional material will be provided by the instructor.

Course Notes & Reading Assignments

All course notes (in pdf format), homeworks, and applets have been moved to the CourseWorks website. If you are registered for this course, it will show up automatically when you log in. If you are not registered and are a Columbia affiliate, you can see all the course material by logging into CourseWorks and searching under "Other Course Listings" using subject code COMS.