RUI: Topics in Computational Geometry

研究将在计算几何中进行五个主题，这是一个涉及设计解决几何问题的有效算法的领域。第一个主题包括找到一种方法来切开和展开多面体，使其平坦而没有重叠的问题。第二个主题是关于在混乱的环境中理解视线的结构。第三个重点是如何将一个固体物体切割成尽可能少的简单碎片。第四个集中在重建（例如）从CAT扫描的肿瘤形状。最后一个主题包括研究机器人手如何安全地抓住一个复杂的物体。每个主题都适合本科生探索。

Research will be performed on five topics in computational geometry, a field concerned with designing efficient algorithms for solving geometric problems. The first topic includes the problem of finding a way to cut open and unfold a polyhedron so that it flattens without overlap. The second topic is concerned with understanding the structure of lines of sight in a cluttered environment. The third focuses on how to cut up a solid object into as few simple pieces as possible. The fourth concentrates on reconstruction of (for example) the shape of a tumor from CAT scans. The final topic includes studying how a robot hand can grasp securely a complex object. Each topic lends itself to exploration by undergraduates.