We present a method for seamless surface parametrization. Recent popular methods first generate a cross-field, where curvature is concentrated at singular vertices. Next, in a separate step, the surface is laid out in the domain subject to derived seamlessness constraints. This decoupling of the process into two independent problems, each with its own objective, leads to suboptimal results. In contrast, our method solves both problems together using domain variables. The key ingredient to the robustness of our method is a rounding strategy based on local estimation. The insight is that testing a small patch to decide between two likely possibilities is a good estimator. Most distortion measures can be used with our method, which get minimized consistently throughout the pipeline. Our method also enables feature alignment, as well as alignment to principle curvatures, and isotropic and anisotropic scaling.

中文翻译：

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直接无缝参数化

我们提出了一种无缝表面参数化的方法。最近流行的方法首先生成一个交叉场，其中曲率集中在奇异顶点处。接下来，在一个单独的步骤中，表面在域中进行布局，并受到派生的无缝约束。将过程解耦为两个独立的问题，每个问题都有自己的目标，导致结果不理想。相比之下，我们的方法使用域变量同时解决了这两个问题。我们方法稳健性的关键因素是基于局部估计的舍入策略。洞察力是测试一个小补丁来决定两种可能的可能性是一个很好的估计。大多数失真测量都可以与我们的方法一起使用，在整个管道中始终保持最小化。我们的方法还可以实现特征对齐，