A novel algorithm that produces a quad layout based on imposed set of singularities is proposed. In this paper, we either use singularities that appear naturally, e.g., by minimizing Ginzburg-Landau energy, or use as an input user-defined singularity pattern, possibly with high valence singularities that do not appear naturally in cross-field computations. The first contribution of the paper is the development of a formulation that allows computing a cross-field from a given set of singularities through the resolution of two linear PDEs. A specific mesh refinement is applied at the vicinity of singularities to accommodate the large gradients of cross directions that appear in the vicinity of singularities of high valence. The second contribution of the paper is a correction scheme that repairs limit cycles and/or non-quadrilateral patches. Finally, a high quality block-structured quad mesh is generated from the quad layout and per-partition parameterization.

中文翻译：

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具有高价奇异性的四边形布局，可实现灵活的四边形网格划分

提出了一种新的算法，该算法基于强加的奇点集产生四边形布局。在本文中，我们要么使用自然出现的奇异点（例如，通过最小化Ginzburg-Landau能量），要么将其用作用户定义的奇异点输入模式，可能具有在跨场计算中不会自然出现的高价奇​​点。本文的第一个贡献是开发了一种公式，该公式允许通过给定的奇点集通过两个线性PDE的解析度来计算跨场。在奇点附近应用特定的网格细化，以适应出现在高价奇点附近的横向大梯度。本文的第二个贡献是一种修正方案，可修复极限环和/或非四边形斑块。最后，