通过对偶环稳健构建多立方体分割
Robust Construction of Polycube Segmentations via Dual Loops
AI总结：
针对自动多立方体分割难以保证有效性的问题，本文提出基于对偶表示的迭代算法 DualCube，可对任意亏格模型持续维护有效分割，并在质量上媲美或超越现有方法。
摘要：
三维模型的多立方体分割可有效支持多种应用，例如无缝纹理映射、样条拟合、结构化多块网格生成以及六面体网格构建。然而，有效多立方体分割的自动化构建存在鲁棒性问题：现有最先进方法无法保证找到有效解。本文提出 DualCube，这是一种迭代算法，保证可为任意亏格的三维模型返回有效的多立方体分割。该算法基于多立方体的对偶表示。从一个具有正确亏格的初始简单多立方体，以及相应的对偶环结构和多立方体分割开始，我们迭代地细化多立方体、环结构和分割，同时保持解的正确性。DualCube 在构造上即具有鲁棒性：在迭代过程中的任意时刻，当前分割都是有效的。此外，其迭代特性有助于在解的质量与复杂度之间实现无缝权衡。DualCube 可使用相对简单的算法构件实现；我们的实验评估表明，所得多立方体分割的质量与最先进方法相当，甚至更优。
英文摘要：
Polycube segmentations for 3D models effectively support a wide variety of applications such as seamless texture mapping, spline fitting, structured multi-block grid generation, and hexahedral mesh construction. However, the automated construction of valid polycube segmentations suffers from robustness issues: state-of-the-art methods are not guaranteed to find a valid solution. In this paper we present DualCube: an iterative algorithm which is guaranteed to return a valid polycube segmentation for 3D models of any genus. Our algorithm is based on a dual representation of polycubes. Starting from an initial simple polycube of the correct genus, together with the corresponding dual loop structure and polycube segmentation, we iteratively refine the polycube, loop structure, and segmentation, while maintaining the correctness of the solution. DualCube is robust by construction: at any point during the iterative process the current segmentation is valid. Its iterative nature furthermore facilitates a seamless trade-off between quality and complexity of the solution. DualCube can be implemented using comparatively simple algorithmic building blocks; our experimental evaluation establishes that the quality of our polycube segmentations is on par with, or exceeding, the state-of-the-art.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
