Workshop on Real Algebraic Geometry in Geometric Modeling

几何建模中的真实代数几何研讨会这个研讨会是关于几何建模和真实代数几何之间当前和潜在的相互作用，特别是真实代数几何，因为它被嵌入在数学科学研究所（MSRI）关于真实代数几何的一个更大的项目中。它于2004年4月3日和4日在MSRI关于实代数几何应用的活动期间举行。研讨会邀请了来自美国和欧洲的专家在本周末和研讨会之后的一周与MSRI社区进行互动。本次研讨会首次探讨了真正的代数几何在几何建模中的作用；几何建模中的基本对象——曲面块或贝塞尔曲线——是真正的代数几何中的对象。它还加强了几何建模和代数几何之间最近互利的相互作用，特别是在隐式化和外来环形表面斑块的发展方面。特别是，环形表面补丁带来的数学挑战需要在它们开始履行其承诺之前得到澄清和解决。这是美国第一个关于这种相互作用的研讨会，将影响美国这些科学联系的演变。

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.