Topics in Computational Geometry: Curved Objects, Restricted-Orientation Objects, Grasping, and Arrangements

Souvaine教授将检查结果在两个直线几何 和一般的几何形状，以确定前者可以是 有效地推广，后者受益于 限制k方向。 许多机器人手由两个 平行的边缘可以移动得更近或更远。 Souvaine教授解释说，所有的多边形都允许在 该模型 她证明了这个猜想并提供了线性时间 算法的特殊类别的多边形。 本研究的目的 是在充分的一般性证明猜想，然后研究 多面体和弯曲物体的相应问题。 在2 最小二乘回归线（LMS）可以是 计算效率。将标准垂直线扫描替换为 拓扑线扫描产生更快的算法。 这些目标 发现计算多维LMS和动态LMS的技术 并确定哪些问题受益于拓扑扫描。

Professor Souvaine will examine results in both rectilinear geometry and general geometry to determine which of the former can be efficiently generalized and which of the latter benefit from a restriction to k orientations. Many robot hands consist of two parallel edges that can move closer together or further apart. Professor Souvaine conjectures that all polygons admit a stable grip in this model. She proved the conjecture and provided linear time algorithms for special classes of polygons. The goal of this research is to prove the conjecture in full generality and then to study the corresponding problems for polyhedra and curved objects. In 2 dimensions, the least median of squares regression line (LMS) can be computed efficiently. Replacing the standard vertical line sweep with a topological line sweep results in a faster algorithm. The goals are to discover techniques for computing multidimensional LMS and dynamic LMS and to determine which problems benefit from topological sweep.