Algorithmic Studies in Applied Geometry

这项研究将产生三个主要影响：(1)为计算几何技术的库添加新的算法和方法，包括新的近似方法和比现有方法更简单和更容易实现的新算法；(2)为相关领域的大量几何问题制定精确的算法版本，使计算几何的方法能够成功地应用，从而使主要是理论计算几何的社区能够适当地接触到该领域的更实际的应用(相关领域包括制图、计算机视觉、计算机辅助设计、图形学、制造、等);(3)向在相关领域工作但基本上不了解计算几何进展的应用研究人员传播计算几何的方法，特别是因为它已被解释为主要的理论工具。第三种影响将通过与工业研究实验室的联系人讨论研究方向，并通过在读者包括广泛的工程学科的会议和期刊上发表论文来产生。

This investigation will have three major impacts: (1) Add new algorithms and methodologies to the repertoire of computational geometry techniques, including new approximation methods and new algorithms that are simpler and easier to implement than existing ones; (2) Formulate precise algorithmic versions of a large body of geometric problems from allied fields, in such a way that the methods of computational geometry can be applied successfully and so that the community of largely theoretical computational geometers can be properly exposed to the more practical applications of the field (allied fields include cartography, computer vision, computer-aided design, graphics, manufacturing, etc); and (3) Disseminate methodologies of computational geometry to applied researchers who work in allied fields but who have been largely unaware of progress in computational geometry, particularly since it has been construed as a primarily theoretical instrument. This third impact will be made through discussions of research directions with contacts in industrial research labs and through publishing papers for conferences and in journals whose readership includes a breadth of engineering disciplines.