Structured meshes, composed of quadrilateral elements in 2D and hexahedral elements in 3D, are widely used in industrial applications and engineering simulations due to their regularity and superior accuracy in finite element analysis. Generating high-quality structured meshes, however, remains challenging, especially for complex geometries and singularities. Field-guided approaches, which construct cross fields in 2D and frame fields in 3D to encode element orientation, are promising but are typically defined on discrete meshes, limiting continuity and computational efficiency. To address these challenges, we introduce \emph{NeurFrame}, a neural framework that represents frame fields continuously over the domain, supporting infinite-resolution evaluation. Trained in a self-supervised manner on discrete mesh samples, NeurFrame produces smooth, high-quality frame fields without relying on dense tetrahedral discretizations. The resulting fields simultaneously guide high-quality quadrilateral surface meshes and hexahedral volumetric meshes, with fewer and better-distributed singularities. By using a single network, NeurFrame also achieves lower computational cost compared to prior self-supervised neural methods that jointly optimize multiple fields.

翻译：结构化网格由二维四边形单元和三维六面体单元构成，因其在有限元分析中具有规则性和更高的精度，被广泛应用于工业场景与工程仿真。然而，生成高质量的结构化网格仍然具有挑战性，尤其对于复杂几何形状和奇异点区域。基于场引导的方法通过构建二维交叉场和三维框架场来编码单元方向，具有较好的前景，但这类方法通常定义在离散网格上，限制了场的连续性并影响计算效率。为解决这些问题，我们提出 \emph{NeurFrame}，一种在计算域上连续表示框架场的神经框架，支持无限分辨率的场值计算。NeurFrame 在离散网格样本上以自监督方式进行训练，无需依赖密集四面体离散化即可生成平滑、高质量的框架场。所得场可同时引导生成高质量的四边形表面网格与六面体体网格，且奇异点数量更少、分布更优。通过使用单一网络，NeurFrame 相比先前联合优化多个场的自监督神经方法，进一步降低了计算成本。