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Host: Mathematical Sciences Research Institute
Homepage: http://www.msri.org/activities/events/9899/mathcad/
Organizers: Hyeong In Choi, Herbert Edelsbrunner, Rida Farouki, David Ferguson, David Hoffman, Helmut Pottmann
Description:
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 3.in relevant mathematical disciplines; 4.promotion of collaborative projects between researchers in the CAD and mathematics communities; and 5.compilation and publication of the workshop findings in an appropriate forum.
Date received: February 23, 1999
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