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

计算几何的重点是设计 来解决几何问题。 这些问题出现在一些 背景，如图形，机器人，医学成像， 制造业 该项目的重点涉及所有这些应用程序 地区 正在审查一些可见性问题，包括 泛光区域和可见度图的结构。 正在探讨的若干问题涉及三个方面： 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（应用于图案 识别）和运动规划配置空间（应用于机器人）。 安排理论中的基本问题正在得到解决。 几 制造业所面对的问题，现正得到处理，包括： 调度冲压工具以在金属板中创建孔的方法， 规定的形状。 女本科生从事各方面工作， 研究和几个有用的软件包正在制作中， 发放

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.