Polycube layouts for 3D models effectively support a wide variety of applications such as hexahedral mesh construction, seamless texture mapping, spline fitting, and multi-block grid generation. However, the automated construction of valid polycube layouts suffers from robustness issues: the state-of-the-art deformation-based methods are not guaranteed to find a valid solution. In this paper we present a novel approach which is guaranteed to return a valid polycube layout for 3D models of genus 0. Our algorithm is based on a dual representation of polycubes; we construct polycube layouts by iteratively adding or removing dual loops. The iterative nature of our algorithm facilitates a seamless trade-off between quality and complexity of the solution. Our method is efficient and can be implemented using comparatively simple algorithmic building blocks. We experimentally compare the results of our algorithm against state-of-the-art methods. Our fully automated method always produces provably valid polycube layouts whose quality - assessed via the quality of derived hexahedral meshes - is on par with state-of-the-art deformation methods.

翻译：多立方体布局对于三维模型能够有效支持多种应用，如六面体网格构建、无缝纹理映射、样条拟合以及多块网格生成。然而，有效多立方体布局的自动构建存在鲁棒性问题：最先进的基于变形的方法无法保证找到有效解。本文提出一种新方法，该方法保证能为零亏格的三维模型返回有效的多立方体布局。我们的算法基于多立方体的对偶表示；通过迭代添加或移除对偶环来构建多立方体布局。算法的迭代性质便于在解的质量与复杂度之间实现无缝权衡。该方法高效且可使用相对简单的算法构建块实现。我们通过实验将算法结果与最先进方法进行对比。我们的全自动方法始终能生成可证明有效的多立方体布局，其质量——通过派生六面体网格的质量进行评估——与最先进的变形方法相当。