Algorithmic Studies in Applied Geometry

计算几何的方法将应用于设计、分析、实现和测试算法，以解决在制造、计算机辅助设计、图形和可视化、机器人、制图和空中交通管制等应用领域出现的问题。这项工作的一个重要方面是向行业传播技术，帮助将算法转化为实践。这将通过寻求新的工业合作来实现，同时在已经建立的几个工业伙伴关系的基础上。为了找到计算几何的应用，以满足工业需求，公司将被访问，以讨论他们的几何计算需求，并制定他们的最关键的问题作为算法问题的实例。此外，随着解决方案的提出和发展，工业合作伙伴将在项目的实施和整合阶段得到协助。具体的问题包括：(a)制造工艺规划（NC验证、刀具轨迹生成、沉积、切割、弯曲）和虚拟制造（碰撞检测、装配规划）；(b)计算机图形学和可视化（绘制大型多边形模型、体可视化、可见性预处理、纹理映射）；(c)地理信息系统，包括在各种限制和目标（空中交通管理、转运、移动机器人、军事任务规划）的几何环境下的地图概化和最佳路线规划。

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).