Algorithmic Studies in Applied Geometry

应用几何中的算法研究

• 批准号: 0098172
• 负责人: Joseph S. Mitchell
• 金额: $ 30万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-09-01 至 2005-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0098172&HistoricalAwards=false
• 关键词: Algorithmic; Studies; Applied; Geometry

Proposal #0098172Mitchell, Joseph S. B.SUNY Stony BrookAlgorithmic Studies in Applied GeometryThe methodologies of computational geometry will be applied to design, analyze, implement, and test algorithms for problems that arise in several application areas, including manufacturing, computer-aideddesign, graphics and visualization, robotics, air traffic management, and cartography. An important aspect of the project is dissemination of the technology to industry, helping to transfer algorithms into practice, while, at the same time, extracting from practitioners a set of high-priority problem areas for further investigation. New industrial collaborations will be pursued, while building on the several industrial partnerships that have already been established. In visitations with practitioners, new applications and mathematical formulations of geometric problems will be developed, and critical algorithmic issues in geometric computation will be identified. Further, as solutions are proposed and developed, the industrialpartners will be assisted with the implementation and integration phases of the projects.The specific repertoire of problems includes: (a) manufacturing process planning (tool path generation, NC verification, bending and folding, deposition, cutting) and virtual manufacturing and maintenance (collision detection, assembly planning); (b) computer graphics and visualization (rendering large polygonal models, data compression, irregular grid volume visualization, visibility preprocessing, optimized texture mapping); (c) Air Traffic Management (conflict detection and resolution, congestion modeling); (d) Mobilerobotics (multiple robot search and exploration); (e) Geographic Information Systems (GIS), including map generalization, optimal route planning in geometric environments under a variety of constraints andobjectives, and network design and optimization (e.g., for fiberless optical networking).

Proposal #0098172Mitchell, Joseph S. B.SUNY Stony BrookAlgorithmic Studies in Applied GeometryThe methodologies of computational geometry will be applied to design, analyze, implement, and test algorithms for problems that arise in several application areas, including manufacturing, computer-aideddesign, graphics and visualization, robotics, air traffic management, and cartography. 该项目的一个重要方面是将技术传播给行业，有助于将算法转移到实践中，同时从从业者那里提取一系列高优先级问题领域，以进行进一步研究。 将在已经建立的几种工业合作伙伴关系的基础上建立新的工业合作。 在与从业人员的访问中，将开发新的应用程序和数学问题，并确定几何计算中的关键算法问题。 此外，随着提出和开发解决方案，工业组件将在项目的实施和集成阶段进行协助。问题的具体曲目包括：（a）制造过程计划（工具路径生成，NC验证，弯曲，折叠，沉积，削减，切割）以及虚拟制造和维护和维护（碰撞检测，组件计划）； （b）计算机图形和可视化（渲染大型多边形模型，数据压缩，不规则网格量可视化，可见性预处理，优化的纹理映射）； （c）空中交通管理（冲突检测和解决，拥塞建模）； （d）MobilerObotics（多个机器人搜索和勘探）； （e）地理信息系统（GIS），包括MAP概括，在各种约束和目标下的几何环境中的最佳路线计划，以及网络设计和优化（例如，用于无光纤光学网络）。