Direct Seamless Parametrization

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.