Inferring Topology and Geometry for Dynamic Shapes

建议：CCF-0830467机构：俄亥俄州立大学PI：Dey，Tamal标题：推断动态形状的拓扑和几何摘要许多科学和工程应用程序都涉及随时间移动、变形和/或演变的三维形状。这些应用程序需要计算方法来模拟运动中的形状，以便进行可视化、检查、原型制作和进一步开发。我们建议将重点放在从适当的表示来推断动态形状的拓扑和几何的问题上。我们认为，根据模拟的目标，用户可以选择维护适当复杂性的数据结构。如果目标是仅捕获拓扑，则可以使用较轻的数据结构，而可以选择更复杂的数据结构来同时捕获几何和拓扑。这一观点产生了过多的数学和算法问题，我们建议在这个项目中进行研究。有理论保证的运动形状的拓扑和几何推理是一个困难而又重要的问题。一个关键挑战是将维护的数据结构的更新成本保持在较低水平。在表面重建和数据分析的背景下对不同类型的复合体进行拓扑分析的最新进展使根据需要以不同的复杂程度表示形状成为可能。在动态环境中有效地使用这些表示法是

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