EAGER: Collaborative Research: Towards Robust and Scalable Hexahedral Meshing

EAGER：协作研究：实现稳健且可扩展的六面体网格划分

• 批准号: 1655306
• 负责人: Mathieu Desbrun
• 金额: $ 10.49万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2016
• 资助国家: 美国
• 起止时间: 2016-09-15 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1655306&HistoricalAwards=false
• 关键词: EAGER; Collaborative; Research; Towards; Robust; EAGER; Collaborative; Research; Towards; Robust

The first step of computer modeling, simulation, or analysis for objects with complex, 3-dimensional geometry is to represent the object as a mesh of simpler objects: (warped) cubes that share faces are the most natural and support many analysis tools, but getting cube faces to match while fitting the geometry is a challenge that causes many tools to use tetrahedra instead. Tetrahedra can be refined locally (replacing one with four, or a touching pair by three) without changing the other faces, but splitting a cube propagates to other cubes, requiring more global insight. This is what this project aims to provide using the concept of "frame fields," with the benefit for better modeling of material and electromagnetic properties of computer-designed and computer-simulated objects. The PIs also plan to continue their work with under-represented groups and with high school students.Frame fields assign coordinate axes in a smooth manner throughout a space. The PIs have done some pioneering work on turning 2d frame fields into quadrilateral surface meshes, and want to explore the possibility of extension to 3d. This project will look to overcome three significant obstacles: 1. The group of symmetries of the cube is more complex than that of the square -- the PIs will explore a representation based on spherical harmonics. 2. The third dimension requires changing sizes and warping where 2d could use unit frame fields -- the PIs will explore sizing and anisotropy fields to fit object gradients. 3. The topology of face-connectedness cubes constrains the mesh -- the PIs will explore the tradeoffs between smooth frames and topology constraints.

计算机建模，仿真或分析具有复杂，3维几何形状的对象的第一步是将对象表示为简单对象的网格：（翘曲）共享面孔的立方体是最自然的，并且支持许多分析工具，但是在拟合几何形状的同时，构成了许多挑战，使许多挑战都可以使用Tetrahedra。 四面体可以在本地进行完善（用四个替换为四个，或者三对三）而不改变其他面，但是将多维数据集散布到其他立方体上，需要更多的全球见解。这是该项目旨在使用“框架字段”的概念提供的，从而更好地建模计算机设计和计算机模拟的对象的材料和电磁特性。 PIS还计划继续与代表性不足的团体和高中生一起继续工作。框架字段在整个空间中以平稳的方式分配坐标轴。 PI在将2D框架字段转换为四边形表面网眼方面做了一些开创性的工作，并希望探索扩展到3D的可能性。 该项目将旨在克服三个重要的障碍：1。多维数据集的对称性组比正方形的对称性更为复杂 - PI将探索基于球形谐波的表示。 2。第三维需要更改尺寸和翘曲，其中2D可以使用单位框架字段 - PIS将探索大小和各向异性字段以适合对象梯度。 3。面部连接的拓扑构成了网格 - PIS将探索平滑框架和拓扑约束之间的权衡。