Algorithmic Studies in Applied Geometry

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The methodologies of computational geometry will be applied to design, analyze, implement, and test algorithms for problems that arise in application areas such as manufacturing, computer-aided design, graphics and visualization, robotics, cartography, and air traffic control. An important aspect of the work is to conduct technology dissemination to industry, helping to transfer algorithms into practice. This will be done through pursuit of new industrial collaborations, while building on the several industrial partnerships that have already been developed. In order to find applications of computational geometry to meet the needs of industry, companies will be visited in order to discuss their geometric computing needs, and formulate their most critical problems as instances of algorithmic questions. Further, as solutions are proposed and developed, the industrial partners will be assisted with the implementation and integration phases of the projects. The specific repertoire of problems includes: (a) manufacturing process planning (NC verification, tool path generation, deposition, cutting, bending) and virtual manufacturing (collision detection, assembly planning); (b) computer graphics and visualization (rendering large polygonal models, volume visualization, visibility preprocessing, texture mapping); (c) Geographic Information Systems (GIS), including map generalization and optimal route planning in geometric environments under a variety of constraints and objectives (air traffic management, transshipment, mobile robotics, military mission planning).