Computation, Visualization and Graphics 1993 Summer Course for Teachers
The Geometry Center
The National Science & Technology Research Center for Computation & Visualization of Geometric Structures
Geometry and the Imagination: Computation, Visualization and Graphics is the title of The Geometry CenterUs 1993 summer course. Computer generated images have become central to our lives. Advertising images, rock videos, and first run movies all use the computer to generate important images. Here you will learn some of the mathematical ideas and computational principles behind the computer generated image.
Course content: Computer generated images are created by combining algorithms for doing a variety of geometric tasks. These algorithms give the computer the ability to do geometry as a human would. We will develop the ideas behind a few geometric algorithms. Ideas will be Rvertically integrated.S That is, we will consider the geometry necessary to model the problem, the data structures used to develop the algorithm, the programs written to implement the algorithm and the images produced by the algorithm. The ideas we develop will build from basic principles, starting from the geometry and computer representation of points, lines and polygons. We will assume that students are conversant with the details of courses in high school geometry and are not averse to computers. Problems involving creating and decomposing complex objects will be presented. The Voronoi diagram data structure, an important modelling structure, will be presented. Ray tracing, the method used to create the images you see on television, will be developed from basic geometric primitives. Artistic considerations that arise in creating satisfying images will be described. All of these ideas will be developed from concepts used in the high school geometry classroom.
Goals: % to understand the nature of geometric computation % to use and modify software for creating graphical images % to examine accessible and interesting examples % to prepare to communicate your understanding to others
Dates and Times: June 21-July 2, 1993, weekdays 9:00 a.m. - 5:00 p.m. Evening and weekend activities will be scheduled.
Eligibility: The course enrollment is limited to 50 students. Up to 30 senior high school teachers will be invited into the program based on application procedures. Applications from middle school teachers with a strong math background and interest are also welcome. The remaining places will be filled by the college students accepted into the ten week research and training program of the Center. Women and underrepresented minorities are especially encouraged to apply. Applications should be received by Feburary 1, 1993 to guarantee consideration.
Credits/Costs: Tuition for the course has been waived. 6 credits for Math 5025 and 5025X through the Extension Division of the University of Minnesota for satisfactory completion of the course. Pass/fail basis only. A $35 registration fee will be due the first day of class if you wish to have credits officially recorded on a transcript. Cost of the transcript is additional.
Prerequisites: It will be assumed that students have some familiarity with computation. A tutorial will be given Sunday, June 20, 1993, to provide students with the appropriate background.
Course materials: There are no assigned texts. Materials will be distributed during class.
Housing: It is highly recommended that all participants stay in the dorms on campus. Past experience and evaluations from former participants show that this is invaluable, even if the participant is a Twin Citian. From Sunday, June 20, through Friday, July 2, air-conditioned housing in double rooms with full meal service will be provided at no charge for all participants who request it at Middlebrook Hall on the West Bank of the University of Minnesota
Travel: Travel allowances of up to $100 for out-of-state teachers will be provided.
David Dobkin is a Professor of Computer Science at Princeton University. His research interests concern the theoretical and practical issues related to doing geometry by computer. David is also deeply involved in the development of curricula at Princeton for computer science education, but his secret fantasy is to be a great basketball player.
Pat Hanrahan is an Associate Professor of Computer Science at Princeton University. His research interests center on the rendering problem, the problem of creating photorealistic images by computer. For a number of years, Pat was Chief Scientist at Pixar (formerly Lucas Films) and has given hundreds of talks presenting graphics to general audiences.
Vibeke Sorenson is director of the Computer Animation Laboratory at the California Institute of the Arts. She is an active computer artist who has shown her work internationally. Vibeke has also worked closely with David in developing curricula.
Diane Souvaine is an Associate Professor of Computer Science at Rutgers University and Associate Director of DIMACS. Her research interests are in computational geometry and practical applications of geometric algorithms. Diane has also been actively involved in developing the DIMACS education program in discrete math for high schools.
For further information, please contact:
The Geometry Center 1300 South Second Street Minneapolis, MN 55454 Phone: (612) 626-0888 Fax: (612) 626-7131 firstname.lastname@example.org
The University of Minnesota is committed to the policy that all persons shall have access to its programs, facilities and employment without regard to race, color, creed, religion, national origin, sex, age, marital status or sexual orientation.
Applications should be submitted by February 1, 1993
Return application for the summer course to: The Geometry Center Summer Course '93 1300 South Second Street Minneapolis, MN 55454
School where teaching:
Ethnicity (circle one): Black Asian Hispanic White Native American Other
Sex (please circle): M F
Yes No I plan to attend the Sunday, June 20, 1992, computer session.
Yes No I plan to stay in the dorm. Please reserve a room for me.
Yes No I will need parking at the dorm.
Attach a short statement concerning your interest in the course and your anticipated classroom use of the materials created.
Attach a statement of support from an appropriate administrator which indicates that you would be able to incorporate these materials into at least one class that you will teach in 1993-94.