Automatic quadrilateral (quad) or hexahedral (hex) multiblock decomposition has been a topic of research for many years. The key challenges are to automatically determine where to place mesh singularities and how to generate a decomposition based on the mesh singularities to get the desired mesh orientation and distribution. In this work, a new idea of achieving these is proposed based on an auxiliary subdivision of the domain into smaller subdomains, followed by applying an equation, which calculates the net number of mesh singularities of a surface, to locate the quad mesh singularities. Under this idea, two different methods are presented based on the medial axis and the inward boundary offset. Both methods are conformal to the vertex classifications of the original domain, which guarantees a good mesh quality at the boundary. The mesh results are compared with a paving method and a cross-field method.

中文翻译：

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通过辅助细分进行四边形多块分解

多年以来，自动四边形（四边形）或六面体（十六进制）多块分解一直是研究的主题。关键的挑战是自动确定在何处放置网格奇点，以及如何基于网格奇点来生成分解以获得所需的网格方向和分布。在这项工作中，提出了一种实现这些目标的新思路，即根据将区域的辅助细分成较小的子域，然后应用方程式来计算曲面的网格奇点的净数目，以定位四边形网格奇点。在这种思想下，基于内侧轴和向内边界偏移提出了两种不同的方法。两种方法都符合原始域的顶点分类，从而保证了边界处的良好网格质量。