Hierarchical Solving of Symbolic Problems in Heterogeneous Geometry Environments

异构几何环境中符号问题的分层求解

• 批准号: 0541402
• 负责人: Elaine Cohen
• 金额: --
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2006
• 资助国家: 美国
• 起止时间: 2006-02-15 至 2010-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0541402&HistoricalAwards=false
• 关键词: Hierarchical; Solving; Symbolic; Problems; Heterogeneous

Hierarchical Solving of Symbolic Problems in Heterogeneous Geometry EnvironmentsPI: Elaine Cohen, Co-PI Richard F. RiesenfeldSchool of Computing, University of UtahAbstractMany important types of problems can be posed in a mathematical form, yet many real-world applications do not provide data in a form that can be used by traditional mathematical solvers. For example, medical models may be made of a 3D volume of point samples rather than the smooth models needed by the mathematical solvers. This research involves unifying these multiple, important methods of representing real-world data with the power of mathematical solvers by using methods based on robust geometry to solve problems. The investigators will use these results in applications for computer prototyping of mechanical systems and for computer-based surgical training. This research should be able to provide such tools as virtual calipers for imaged tumors or force-feedback interaction with complex medical data in the medical realm, and checking the fit of a CAD modeled mechanical part with a laser-scanned real part in the engineering realm.This research proposes to use hierarchical, geometric representations to compute solutions of symbolic problems, thereby expanding the applicability of symbolic solvers to areas where the data may not be in the form of equations. Examples of such applications include real-world applications in engineering and medicine. Because this approach relies on bounds to intrinsic geometric properties, rather than manipulating only the underlying representations directly, the approach also will allow a single application problem to have several different model representations mixed together. This arises in complex problems where some data may be analytical, some acquired, and some just rough approximations.

异构几何环境中符号问题的分层求解PI：Elaine Cohen，联合PI Richard F. Riesenfeld 犹他大学计算学院摘要许多重要类型的问题可以以数学形式提出，但许多实际应用程序并不以传统数学求解器可以使用的形式提供数据。例如，医学模型可能由 3D 体积的点样本组成，而不是数学求解器所需的平滑模型。这项研究涉及通过使用基于稳健几何的方法来解决问题，将这些表示现实世界数据的多种重要方法与数学求解器的能力相结合。研究人员将把这些结果用于机械系统的计算机原型设计和基于计算机的外科手术训练。这项研究应该能够提供诸如用于成像肿瘤的虚拟卡尺或在医学领域中与复杂医疗数据进行力反馈交互等工具，以及在工程领域中检查 CAD 建模机械零件与激光扫描真实零件的配合性。这项研究建议使用分层几何表示来计算符号问题的解决方案，从而将符号求解器的适用性扩展到数据可能不存在的领域。 方程的形式。 此类应用的示例包括工程和医学领域的实际应用。由于这种方法依赖于内在几何属性的界限，而不是仅直接操作底层表示，因此该方法还允许单个应用程序问题将多个不同的模型表示混合在一起。 这出现在复杂的问题中，其中一些数据可能是分析数据，一些数据可能是获得的，而一些数据只是粗略的近似值。