This is a local copy. Source is http://www.msri.org/activities/events/9899/mathcad/.
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.
We have arranged the following list of speakers and topics for the position papers:
In Choi, Seoul National University
"Applications of geometric algebras in CAD"
Herbert Edelsbrunner, University of Illinois
"Computational geometry and discrete mathematics in CAD"
Farin, Arizona State University
"CAGD: state of the art, open problems, and new possibilities"
Goodman, University of Dundee
"Splines, subdivision methods, and wavelets"
McCarthy, University of California, Irvine
"Constraint manifolds and the geometry of motion"
Pottmann, Technical University of Vienna
"Applications of special geometries in CAD"
Strotman, Structural Dynamics Research Corporation
"Mathematical problems in CAD software development"
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 (email@example.com) 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 (firstname.lastname@example.org), or by
postal mail to:
Department of Mechanical and Aeronautical Engineering,
Davis, CA 95616
Attn: Mathematical Foundations of CAD workshop
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