中文摘要：

四边形、六面体网格具有良好的局部单元特性和整体拓扑性质,其在几何处理、有限元计算等大量的应用中有着不可替代的优势.然而,这些应用对所生成的网格有很高的要求,如要求较低的形状误差、较高的单元质量、较少的单元格数、较优的拓扑结构等.这些要求对生成符合特定应用需求的网格提出了巨大的挑战.这些要求之间存在冲突和制约,因而很难获得满足所有要求的网格.生成符合特定应用需求的这种网格有着巨大的挑战.文中从流形网格参数化的视角,系统地介绍近些年来典型的自动优化方法,分析相关技术的优缺点,讨论并给出了当前面临的主要技术挑战和今后发展方向.

英文摘要：

Quadrilateral and hexahedral meshes have irreplaceable advantages in geometry processing, finite element analysis and many other applications because of their excellent element properties and global topology structure. However, there are great challenges to generate such meshes under various requirements raised from the applications, for example low shape approximation error, high cell quality, small number of cells and good topology structure. These requirements often conflict with each other, which makes it hard to find a mesh satisfying all these requirements. In this paper, we systematically introduce the typical recent automatic methods from the view point of manifold parameterization, and analyze their advantages and limitations, then discuss the current major challenges and future works.