Polycube structures provide parametric domains for all-hexahedral (all-hex) mesh generation and analysis-suitable volumetric spline construction in isogeometric analysis (IGA). Recent learning-based polycube pipelines have improved automation, yet several challenges remain when handling complex CAD geometries. These challenges include the limited diversity of primitive geometries, restricted grid configurations, and the increasing cost of genus-guided context search during inference as both the primitive set and the grid size grow. In this paper, we present {Scalable DDPM-Polycube}, an extended diffusion-based polycube construction method that addresses these limitations. First, we expand the primitive set from two primitive geometries to three by introducing a blind-hole cube primitive, thereby improving the representation of local hole-like features that do not change the global genus. Second, we extend the grid configuration from the previous $2\times 1$ setting to an enlarged three-dimensional grid configuration, which increases representational capacity and reduces mapping distortion for complex geometries. Third, we develop a genus-guided context generation strategy together with a hierarchical verification procedure, enabling robust context generation in both user-guided and automated modes. Once a valid polycube structure is generated, it is used for parametric mapping, all-hex control mesh generation, and volumetric spline construction. Experimental results demonstrate that scalable DDPM-Polycube improves the generality, scalability, and automation of diffusion-based polycube generation, and supports hex mesh generation and volumetric spline construction for IGA applications on complex geometries.

翻译：多立方体结构为等几何分析中的全六面体网格生成与分析适用体积样条构造提供了参数域。近年来基于学习的多立方体流水线虽提升了自动化程度，但在处理复杂计算机辅助设计几何体时仍面临若干挑战，包括基元几何多样性有限、网格配置受限，以及推理过程中随基元集和网格尺寸增长而增加的类属引导上下文搜索成本。本文提出可扩展扩散式多立方体构造方法——Scalable DDPM-Polycube，旨在解决上述局限性。首先，通过引入盲孔立方体基元，将基元集从两种基元几何扩展至三种，从而增强对不改变全局亏格的局部孔状特征的表示能力。其次，将网格配置从先前的2×1设置扩展为三维增强网格配置，提升了复杂几何的表示容量并降低了映射畸变。第三，开发了类属引导的上下文生成策略与分层验证流程，可在用户引导与自动化两种模式下实现鲁棒的上下文生成。生成有效的多立方体结构后，将其用于参数映射、全六面体控制网格生成及体积样条构造。实验结果表明，可扩展DDPM-Polycube提升了扩散式多立方体生成的通用性、可扩展性与自动化程度，并能在复杂几何上为等几何分析应用提供六面体网格生成与体积样条构造支持。