Inferring Topology and Geometry for Dynamic Shapes

推断动态形状的拓扑和几何形状

• 批准号: 0830467
• 负责人: Tamal Dey
• 金额: $ 22万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-09-01 至 2011-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0830467&HistoricalAwards=false
• 关键词: Inferring; Topology; Geometry; Dynamic; Shapes

Proposal: CCF- 0830467Institution: Ohio State UniversityPI: Dey, TamalTitle: Inferring Topology and Geometry for Dynamic ShapesABSTRACTMany applications in science and engineering deal with three dimensional shapes that move, deform, and/or evolve with time. These applications need computational methods to simulate such shapes in motion for visualization, inspection, prototyping, and further developments. We propose to focus on the problem of inferring topology and geometry of a dynamic shape from an appropriate representation. We argue that the user can be given a choice of maintaining a data structure of appropriate complexity depending on the goal of the simulation. A lighter data structure can be used if the goal is to capture only topology whereas a more complex data structure can be chosen for capturing both geometry and topology. This view point generates a plethora of mathematical and algorithmic questions that we propose to investigate in this project. Topology and geometry inference of shapes in motion with theoretical guarantee is a difficult but important problem. A key challenge is to keep the update costs for the maintained data structures low. Recent developments in topological analysis of different types of complexes in the context of surface reconstruction and data analysis have opened up the possibility of representing a shape at different levels of complexity depending on the need. An efficient use of these representations in a kinetic setting is

提案：CCF-0830467机构：俄亥俄州州立大学PI：Dey，Tamal题目：推断动态形状的拓扑和几何摘要在科学和工程中的许多应用涉及随着时间移动、变形和/或演化的三维形状。这些应用需要计算方法来模拟运动中的这些形状，以进行可视化，检查，原型设计和进一步开发。 我们建议把重点放在从一个适当的表示推理的动态形状的拓扑结构和几何形状的问题。我们认为，用户可以选择维护一个适当的复杂性的数据结构，这取决于模拟的目标。如果目标是仅捕获拓扑，则可以使用更轻的数据结构，而可以选择更复杂的数据结构来捕获几何和拓扑。这个观点产生了大量的数学和算法问题，我们建议在这个项目中进行调查。运动物体的拓扑和几何推理是一个有理论保证的困难而重要的问题。一个关键的挑战是保持维护数据结构的更新成本较低。最近的事态发展，在拓扑分析的不同类型的复杂的表面重建和数据分析的背景下，开辟了可能性，表示形状在不同层次的复杂性取决于需要。在动态环境中有效使用这些表示是