We introduce a conceptually simple and efficient algorithm for seamless parametrization, a key element in constructing quad layouts and texture charts on surfaces. More specifically, we consider the construction of parametrizations with prescribed holonomy signatures i.e., a set of angles at singularities, and rotations along homology loops, preserving which is essential for constructing parametrizations following an input field, as well as for user control of the parametrization structure. Our algorithm performs exceptionally well on a large dataset based on Thingi10k [Zhou and Jacobson 2016], (16156 meshes) as well as on a challenging smaller dataset of [Myles et al. 2014], converging, on average, in 9 iterations. Although the algorithm lacks a formal mathematical guarantee, presented empirical evidence and the connections between convex optimization and closely related algorithms, suggest that a similar formulation can be found for this algorithm in the future.

翻译：本文提出了一种概念简洁且高效的无缝参数化算法，该算法是构建曲面四边形布局与纹理图集的关键要素。具体而言，我们研究如何构造具有指定全纯特征的参数化，即在奇异点处预设角度集合同沿同调环路的旋转量。保持这些特征对于依据输入场构建参数化以及实现用户对参数化结构的控制至关重要。我们的算法在基于Thingi10k [Zhou and Jacobson 2016] 的大规模数据集（16156个网格）以及[Myles et al. 2014]提出的高难度小规模数据集上均表现优异，平均收敛仅需9次迭代。尽管该算法目前缺乏严格的数学保证，但所呈现的经验证据及其与凸优化及密切关联算法之间的理论联系表明，未来有望为此算法建立类似的形式化理论框架。