We present a method for generating orthogonal quadrilateral meshes subject to user-defined feature alignment and sizing constraints. The approach relies on computing integrable orthogonal frame fields, whose symmetries are implicitly represented using orthogonally decomposable (odeco) tensors. We extend the existing 2D odeco integrability formulation to the 3D setting, and define the useful energies in a finite element approach. Our frame fields are shear-free (orthogonal) by construction, and we provide terms to minimize area and/or stretch distortion. The optimization naturally creates and places singularities to achieve integrability, obviating the need for user placement or greedy iterative methods. We validate the method on both smooth surfaces and feature-rich CAD models. Compared to previous works on integrable frame fields, we offer better performance in the presence of mesh sizing constraints and achieve lower distortion metrics.

翻译：我们提出了一种生成正交四边形网格的方法，该方法可满足用户定义的特征对齐与尺寸约束。该方法依赖于计算可积正交标架场，其对称性通过正交可分解张量隐式表示。我们将现有的二维正交分解可积性公式扩展到三维场景，并通过有限元方法定义了有效的能量项。所构造的标架场具有无剪切（正交）特性，我们提供了用于最小化面积和/或拉伸畸变的项。优化过程自然生成并定位奇异点以实现可积性，避免了用户手动放置或贪心迭代方法的需求。我们在光滑曲面和富含特征的CAD模型上验证了该方法。与以往关于可积标架场的研究相比，我们在存在网格尺寸约束的情况下展现出更优的性能，并实现了更低的畸变度量指标。