Algorithms design for motion problems: theory & practice

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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.