Sheraton Old Town Hotel
Albuquerque, New Mexico
Institute of Geometry, Vienna University of Technology, Austria
Recent research has demonstrated the effectiveness of using classical geometric methods for the solution of problems arising in Computer-Aided Design. Because of a poor coverage of classical geometry in most mathematics curricula and the lack of suitable textbooks, the promising results that have been obtained so far have been fully understood only by a rather limited number of experts. On the other hand, the results of geometry driven research have received a lot of interest and are well suited for inclusion in professional systems. Thus it seems a good idea to offer a course that aims at an introduction to central concepts of classical geometry and their applications in CAD.
Classical geometric methods have been successfully applied to a variety of problems in Computer-Aided Design and Geometric Modeling, such as sweep surface design, animation and robot motion planning, segmentation and surface fitting in reverse engineering and NURBS representations of special functional forms of curves and surfaces (offsets, developable surfaces, blending surfaces,...). The applied classical material is located in a broad area, which includes projective geometry and classical differential geometry in its center and is surrounded by line geometry, sphere geometry, algebraic geometry, kinematical geometry and other geometric disciplines.
The course introduces to central concepts from these fields with a particular emphasis on projective geometry and demonstrates its use in Computer-Aided Design.
The attendee will get an understanding of the most basic concepts in classical geometry, their computational treatment and their application in solving CAD problems. This should enable the attendee to better identify the area in which a geometric problem should be treated and it should help to better understand and to implement recently developed algorithms in this field.
Intermediate 30 %
Advanced 20 %
Researchers, developers in industry and educators who wish to gain better understanding of central classical geometric concepts and their application in Computer-Aided Design and Geometric Modeling.
Linear algebra, calculus, basics of elementary differential geometry, basics of Bézier- and B-spline techniques.
8:00 AM-11:00 AM Registration
9:00 AM - 9:15
9:15 AM - 10:15
AM Basics of Projective Geometry
10:15 AM - 10:45 AM Coffee
10:45 AM - 11:30
AM Applications of Duality
11:30 AM - 12:30
PM Geometric Approximation
Martin Peternell and Helmut Pottmann
12:30 PM - 2:00 PM Lunch
2:00 PM - 3:00
PM Kinematical Geometry and Motion Design
3:00 PM - 4:00
PM Sphere Geometry with Applications
4:00 PM - 4:30 PM Coffee
4:30 PM - 5:30
PM Segmentation and Surface Fitting in Reverse Engineering
5:30 PM Short Course adjourns
Seats are limited. We urge attendees to register in advance. To register, please submit the on-line preregistration form. Payment should reach the SIAM office on or before October 11, 1999.
Registration fee for the short course includes short course notes, coffee breaks, and lunch on Saturday, November 6.
Short Course Classes: Turquoise Room
Coffee Breaks: Potters Room
Lunch: Weavers Room
Created 6/7/99, Updated 6/15/99