We propose a method for computing integrable orthogonal frame fields on planar surfaces. Frames and their symmetries are implicitly represented using orthogonally decomposable (odeco) tensors. To formulate an integrability criterion, we express the frame field's Lie bracket solely in terms of the tensor representation; this is made possible by studying the sensitivity of the frame with respect to perturbations in the tensor. We construct an energy formulation that computes smooth and integrable frame fields, in both isotropic and anisotropic settings. The user can prescribe any size and orientation constraints in input, and the solver creates and places the singularities required to fit the constraints with the correct topology. The computed frame field can be integrated to a seamless parametrization that is aligned with the frame field.

翻译：本文提出一种在平面曲面上计算可积分正交标架场的方法。标架及其对称性通过正交可分解（odeco）张量隐式表示。为构建可积分性准则，我们仅利用张量表示表达标架场的李括号；这一突破源于对标架关于张量扰动的敏感性分析。我们构建了一个能量函数，能够在各向同性与各向异性场景中计算光滑且可积分的标架场。用户可输入任意尺寸与方向约束，求解器将自动生成并布置满足拓扑约束所需的奇异点。计算所得的标架场可进一步积分，生成与标架场对齐的无缝参数化曲面。