Algorithms design for motion problems: theory & practice

运动问题是计算几何研究的基本问题之一，在各种应用领域都有出现。这些领域包括：变形、拓扑匹配、创建虚拟卷尺以测量沿遗产对象表面的沿着距离、避免危险天气的飞行计划、用于生成道路计划的方法、以及对用于生物医学应用的最佳波束治疗进行建模。我们建议提供的理论和实践基础的算法，解决有关的问题，计算最短路径的情况下，路径通过非均匀介质。我们将特别解决域动态变化的问题，就像许多应用程序中的情况一样。我们计划通过提供一个实现算法的工具箱来使我们的方法对其他研究人员可用。我们还建议研究涉及路径之间距离的问题，例如，如果阿尔茨海默氏症患者明显偏离他/她通常采取的路线，在这种情况下，手机可能会触发警报。

Movement problems are among the fundamental problems studied in computational geometry and arise in a variety of applications areas. These areas include: morphing, topology matching, creation of a virtual tape measure to measure distances along surfaces of heritage objects, flight planning avoiding hazardous weather, methods for generating road plans, and modeling optimal beam treatment for bio-medical applications. We propose to provide the theoretical and practical foundations for algorithms that solve problems related to computing shortest paths in scenarios where the paths travel through non-homogeneous media. We will address in particular problems where the domain is dynamically changing, as is the case in many applications. We plan to make our methods accessible to other researchers by providing a tool-box of implemented algorithms. We also propose to study problems involving distances between paths which could e.g., be useful to see if an Alzheimer's patient is deviating significantly from a route that he/she is typically taking. In that case, a cellphone could trigger an alarm.