RUI: Topics in Computational Geometry

计算几何的重点是设计求解几何问题的算法。它们出现在许多应用环境中，包括制造、图形绘制、机器人和图形。该项目的重点涉及所有这些应用领域。多面体上最短路径和测地线的研究涉及到机器人技术和图形学中的纹理映射。研究的折叠和展开与各种制造问题有关。可见性算法在图形和图形绘制中也有应用。我们将从理论上和通过代码实验来研究这些领域的一系列基本开放问题。在测地线、折叠、泛光灯照明和能见度图方面可以取得进展。女本科生将参与研究的各个方面，所有开发的软件将在互联网上免费发布。

The focus of computational geometry is designing algorithms for solving geometric problems. These arise in a number of application contexts, including manufacturing, graph drawing, robotics, and graphics. The project's concentrations touch on all these application areas. Research on shortest paths and geodesics on polytopes is relevant to robotics and to texture mapping in graphics. Folding and unfolding of research is connected to a variety of manufacturing concerns. And visibility algorithms see use in graphics and graph drawing. A collection of fundamental open problems in these areas will be pursued, both theoretically and through experimentation with code. Progress on geodesics, on folding, on floodlight illumination, and on visibility graphs can be expected. Female undergraduate students will be engaged in all aspects of the research, and all software developed will be freely distributed on the Internet.