GD99 Short Course on Applications of Classical Geometry in Computer-Aided Design

Saturday, November 6, 1999

Sheraton Old Town Hotel
Albuquerque, New Mexico


Helmut Pottmann
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.

Course Objectives

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.

Level of Material

Introductory 50 %
Intermediate 30 %
Advanced 20 %

Who Should Attend

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.

Recommended Background

Linear algebra, calculus, basics of elementary differential geometry, basics of Bézier- and B-spline techniques.


Helmut Pottmann
is a Professor of Mathematics at Vienna University of Technology. He received a PhD from TU Vienna and has had faculty positions at Purdue University, University of Hamburg and University of Kaiserslautern. His research focuses on applications of classical geometry in CAD/CAM, geometric modeling, robot kinematics and scientific visualization. He is associate editor of "Computer Aided Geometric Design" and "Computing" and Vice Chair of the SIAM Activity Group on Geometric Design.

Bert Juettler
studied Mathematics at the Universities of Technology Dresden and Darmstadt. He graduated as a Diplom-Mathematiker in 1992 and gained a PhD in 1994, both from Darmstadt. From 1994 to 1996 he was a postdoctoral research assistant in Darmstadt and at the University of Dundee, Scotland. Currently he is a Lecturer at the Department of Mathematics, Darmstadt University of Technology. His research interests include classical geometry, computer aided geometric design, robotics and kinematics.

Stefan Leopoldseder
studied Mathematics and Descriptive Geometry at Vienna University of Technology, where he received his PhD in 1998. Currently he is a Lecturer at TU Vienna. His research focuses on applications of classical geometry in computer aided design and geometric modeling.

Martin Peternell
is currently a University Assistant at Vienna University of Technology. He studied Mathematics and Descriptive Geometry at TU Vienna and received his PhD in 1997. His research interests are in applied geometry and geometric computing.



8:00 AM-11:00 AM Registration

9:00 AM - 9:15 AM Introduction
Helmut Pottmann

9:15 AM - 10:15 AM Basics of Projective Geometry
Helmut Pottmann

10:15 AM - 10:45 AM Coffee

10:45 AM - 11:30 AM Applications of Duality
Stefan Leopoldseder

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
Bert Juettler

3:00 PM - 4:00 PM Sphere Geometry with Applications
Martin Peternell

4:00 PM - 4:30 PM Coffee

4:30 PM - 5:30 PM Segmentation and Surface Fitting in Reverse Engineering
Helmut Pottmann

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.


Registration: Kachina Room
Short Course Classes: Turquoise Room
Coffee Breaks: Potters Room
Lunch: Weavers Room

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