We present a method for constructing seamless parametrization for surfaces of any genus that can handle any feasible cone configuration with any type of cones. The mapping is guaranteed to be locally injective, which is due to careful construction of a simple domain boundary polygon. The polygon’s complexity depends on the cones in the field, and it is independent of mesh geometry. The result is a small polygon that can be optimized prior to the interior mapping, which contributes to the robustness of the pipeline.

For a surface of genus >0, non-contractible loops play an important role, and their holonomies significantly affect mapping quality. We enable holonomy prescription, where local injectivity is guaranteed. Our prescription, however, is limited and cannot handle all feasible holonomies due to monotonicity constraints that keep our polygon simple. Yet this work is an important step toward fully solving the holonomy prescription problem.

我们提出了一种为任何属的表面构建无缝参数化的方法，该方法可以处理任何类型锥体的任何可行锥体配置。该映射保证是局部单射的，这是由于仔细构造了简单的域边界多边形。多边形的复杂性取决于场中的锥体，并且与网格几何形状无关。结果是一个小多边形，可以在内部映射之前进行优化，这有助于管道的稳健性。

对于亏格 >0 的表面，不可收缩环起着重要作用，并且它们的完整性显着影响映射质量。我们启用完整处方，保证局部注入性。然而，我们的规定是有限的，并且由于单调性约束使我们的多边形保持简单，因此无法处理所有可行的完整。然而，这项工作是朝着完全解决完整处方问题迈出的重要一步。