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Workshop on Mathematical Foundations of CAD

at the Mathematical Sciences Research Institute, Berkeley, CA

June 4-5, 1999

Algorithms for the representation and manipulation of geometry in computer aided design (CAD) systems incur problems with deep roots in many areas of classical mathematics, such as algebraic and differential geometry, topology, analysis, and approximation theory. Examples include methods for computing the space curves defined by intersections of algebraic surfaces, for constructing smooth "blends" that join given surfaces with tangent/curvature continuity, and for developing "topologically faithful" rational approximations, satisfying a prescribed geometrical tolerance, to non-rational loci. The absence of rigorous and reliable solutions to such problems has been a serious impediment to the efficient and systematic use of CAD software in engineering practice.

Although CAD has developed rapidly over the past 20 years, much of this advance has occurred without a meaningful and sustained dialog with the relevant research communities in pure mathematics, and the fundamental problems identified above have been bypassed by resorting to expedient heuristic methods. There is a widespread perception that the performance of CAD systems has now reached a rather unsatisfactory plateau of efficiency and reliability, that can only be surpassed through a re-assessment of the mathematical foundations and the introduction of new mathematical paradigms.

The purpose of this workshop is to stimulate discussion and promote interaction between the CAD and mathematics communities, by bringing together small groups of leading researchers in the two fields. The emphasis will be exploratory in nature, with "position papers" used to stimulate discussion concerning current needs, possibilities, and promising areas for joint exploration. The anticipated outcomes of the workshop include: (1) exposing mathematicians to an interesting array of geometry problems motivated by CAD needs; (2) imparting to the CAD algorithm developers an idea of the current state-of-the-art in relevant mathematical disciplines; (3) promotion of collaborative projects between researchers in the CAD and mathematics communities; and (4) compilation and publication of the workshop findings in an appropriate forum.


The meeting will be organized as a set of "focus sessions" on specific technical topics. Each focus session will comprise a "position paper" presented by an authority in that area, shorter technical papers, and a open discussion period.

The workshop program is available.

We have arranged the following list of speakers and topics for the position papers:

 Hyeong In Choi, Seoul National University
"Applications of geometric algebras in CAD"

 Herbert Edelsbrunner, University of Illinois
"Computational geometry and discrete mathematics in CAD"

 Gerald Farin, Arizona State University
"CAGD: state of the art, open problems, and new possibilities"

 Tim Goodman, University of Dundee
"Splines, subdivision methods, and wavelets"

 Mike McCarthy, University of California, Irvine
"Constraint manifolds and the geometry of motion"

 Helmut Pottmann, Technical University of Vienna
"Applications of special geometries in CAD"

 Tim Strotman, Structural Dynamics Research Corporation
"Mathematical problems in CAD software development"

 John Sullivan, University of Illinois
"Computational differential geometry"

If you would like to present a technical paper (about 15-20 minutes) that falls in any of these areas, please send a title and abstract to Rida Farouki, UC Davis ( by May 7th.

Some support for travel and local expenses is available. To apply for financial support or for waiver of the registration fee, send a letter explaining your interest in the workshop together with a brief vita or bibliography, and an estimate of your request for funds. Students should solicit a letter from a faculty advisor for their application. Applications for financial support will be considered on a rolling basis. Early submission is strongly encouraged. To apply for financial support, please send your materials to Rida Farouki (, or by postal mail to:

Rida Farouki,
Department of Mechanical and Aeronautical Engineering,
UC Davis,
Davis, CA 95616
Attn: Mathematical Foundations of CAD workshop

Transportation from local airports
Directions to MSRI and Saturday bus service
Visa information for foreign visitors


To Register, Participants should send their registration either by email to by fax to: (510) 642-8609, or by regular mail to:

Mathematical Foundations of CAD
Mathematical Sciences Research Institute
1000 Centennial Drive
Berkeley, CA 94720-5070.

Registration fee is $100 per person. Registration fees will be waived for students and postdocs. Payment may be made by check (drawn on a US bank) or credit card (Mastercard, Visa). Please mail payment with your registration form. Registration is open through May 17, 1999, subject to availability. Applications for attendance will be accepted after May 17, space permitting.

Last Updated 5/12/99, K. Garrett