RUI: Visibility, 3D, and Other Topics in Computational Geometry

计算几何的核心是为解决几何问题而设计。这些问题出现在许多环境中，例如图形、机器人、医学成像和制造。该项目的重点涉及所有这些应用领域。正在审查一些能见度问题，包括用泛光灯覆盖区域，以及能见度图表的结构。正在探索的几个问题涉及三个维度：从平行切片重建(及其在图形变形中的应用)，计算集合的直径和中心点(应用于模式识别)，以及运动规划配置空间(应用于机器人学)。正在讨论安排理论中的基本问题。制造业产生的几个问题正在得到解决，包括安排一个冲压工具在规定形状的金属板上打一个洞的问题。女本科生从事这项研究的方方面面，正在制作和分发几个有用的软件包。

The focus of computational geometry is designing for solving geometric problems. These arise in a number of contexts, such as graphics, robotics, medical imaging, and manufacturing. The project's concentrations touch on all these application areas. A number of visibility questions are being examined, including covering regions with floodlights, and the structure of visibility graphs. Several of the problems being explored involve three dimensions: reconstruction from parallel slices (and its application to graphics morphing), computing diameters and centerpoints of sets (with applications to pattern recognition), and motion planning configuration spaces (application to robotics). Fundamental questions in the theory of arrangements are being addressed. Several problems arising from the manufacturing community are being tackled, including that of scheduling a punching tool to create a hole in a sheet of metal of a prescribed shape. Female undergraduate students are engaged in all aspects of the research, and several useful software packages are being produced and distributed.