Topology-aware hexahedral mesh generation based on singularities of3D tensor fields

本研究计画的目的是针对输入的二维与三维物体，提出一个四边形与六面体网格分解的演算法。这是一个重要的过程，将输入对象转换为离散表示，特别是有限元方法分析。我们的想法是在输入对象内合成一个适当的张量场，并通过定位底层张量场的退化来控制整个网格拓扑。这无疑将引导我们生成高质量的四边形和六面体网格。

This research project aims at composing an algorithm fordecomposing the input 2D and 3D objects quadrilateral and hexahedral meshes, which aresets of quadrilaterals and hexahedra. This is an important process for transforming inputobjects into their discrete representations especially for finite element method analysis.Our idea is to synthesize an appropriate tensor field within the input object, and controlthe overall mesh topology by locating the degeneracy on the underlying tensor field. Thissuccessfully leads us to the generation of high-quality quadrilateral and hexahedralmeshes.