Workshop on Real Algebraic Geometry in Geometric Modeling

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Workshop on Real Algebraic Geometry in Geometric ModelingThis workshop is on the current and potential interactions between geometric modeling and real algebraic geometry, particularly real algebraic geometry, as it is embedded in a larger program at the Mathematical Sciences Research Institute (MSRI) on real algebraic geometry. It is held on April 3 and 4, 2004 during a period of activity at MSRI on applications of real algebraic geometry. The workshop brings experts from the United States and Europe to interact with the MSRI community for this weekend and the week following the workshop.This workshop explores, for the first time, the role of real algebraic geometry in geometric modeling; the basic objects in geometric modeling---surface patches or a Bezier curves---are objects in real algebraic geometry. It also strengthens recent, mutually beneficial interactions between geometric modeling and algebraic geometry, specifically in implicitization and the development of exotic toric surface patches. In particular, there are mathematical challenges posed by toric surface patches that need to be clarified and addressed before they can begin to fulfill their promise. This is first workshop in the US on such interactions and will influence the evolution of these scientific links in US.