Polycube layouts for 3D models effectively support a wide variety of methods such as hex-mesh construction, seamless texture mapping, spline fitting, and multi-block grid generation. Our study of polycube layouts is motivated by conformal mesh generation for aerospace modelling. In this setting, quality and correctness guarantees are of the utmost importance. However, currently the fully automatic construction of valid polycube layouts still poses significant challenges: state-of-the-art methods are generally not guaranteed to return a proper solution, even after post-processing, or they use a prohibitively large number of voxels that add detail indiscriminately. In this paper we present a robust, flexible, and efficient method to generate polycube layouts. Our approach is based on a dual representation for polycube layouts and builds a layout by iteratively adding dual loops. Our construction is robust by design: at any iterative step we maintain a valid polycube layout. We offer the flexibility of manual intervention if the user so desires: while our method is able to compute a complete polycube layout without user intervention, the user can interrupt after each iteration and target further refinement on both the local and the global level. Last but not least, our method is efficient and can be implemented using comparatively simple algorithmic building blocks. Our implementation is publicly available and we present its output for numerous benchmark models.

翻译：三维模型的多立方体布局有效支持多种方法，例如六面体网格构建、无缝纹理映射、样条拟合和多块网格生成。我们对多立方体布局的研究源于航空航天建模中的保形网格生成需求。在此场景中，质量和正确性保证至关重要。然而，目前全自动构建有效多立方体布局仍面临重大挑战：现有方法即使在后处理后通常也无法保证返回正确解，或使用数量过多且不加区分添加细节的体素。本文提出一种稳健、灵活且高效的多立方体布局生成方法。我们的方法基于多立方体布局的对偶表示，通过迭代添加双环逐步构建布局。该构建方法在设计上具有稳健性：任何迭代步骤均保持有效多立方体布局。若用户需要，我们提供手动干预的灵活性：虽然方法无需用户干预即可计算完整布局，但用户可在每次迭代后中断，并在局部和全局层面进行定向细化。最后需指出，我们的方法高效且可通过相对简单的算法模块实现。相关实现已公开，并展示了其对众多基准模型的输出结果。