We develop an optimization-based method to model smocking, a surface embroidery technique that provides decorative geometric texturing while maintaining stretch properties of the fabric. During smocking, multiple pairs of points on the fabric are stitched together, creating non-manifold geometric features and visually pleasing textures. Designing smocking patterns is challenging, because the outcome of stitching is unpredictable: the final texture is often revealed only when the whole smocking process is completed, necessitating painstaking physical fabrication and time consuming trial-and-error experimentation. This motivates us to seek a digital smocking design method. Straightforward attempts to compute smocked fabric geometry using surface deformation or cloth simulation methods fail to produce realistic results, likely due to the intricate structure of the designs, the large number of contacts and high-curvature folds. We instead formulate smocking as a graph embedding and shape deformation problem. We extract a coarse graph representing the fabric and the stitching constraints, and then derive the graph structure of the smocked result. We solve for the 3D embedding of this graph, which in turn reliably guides the deformation of the high-resolution fabric mesh. Our optimization based method is simple, efficient, and flexible, which allows us to build an interactive system for smocking pattern exploration. To demonstrate the accuracy of our method, we compare our results to real fabrications on a large set of smocking patterns

翻译：我们提出了一种基于优化的方法来模拟褶绣——一种既能提供装饰性几何纹理又能保持织物拉伸特性的表面刺绣技术。在褶绣过程中，织物上的多组点对被缝合在一起，产生非流形几何特征和视觉上令人愉悦的纹理。设计褶绣图案具有挑战性，因为缝合结果难以预测：最终纹理往往只有在整个褶绣过程完成后才能显现，这导致需要繁琐的物理制作和耗时的试错实验。这促使我们探索数字褶绣设计方法。直接尝试使用表面变形或布料模拟方法计算褶绣织物几何形状无法产生逼真结果，这可能是由于设计的复杂结构、大量接触点以及高曲率褶皱。我们转而将褶绣建模为图嵌入和形状变形问题。我们提取一个表示织物和缝合约束的粗粒度图，然后推导出褶绣结果的图结构。我们求解该图的三维嵌入，进而可靠地指导高分辨率织物网格的变形。我们的基于优化的方法简单、高效且灵活，使我们能够构建一个用于褶绣图案探索的交互式系统。为了证明我们方法的准确性，我们将结果与大量褶绣图案的实际制作进行了比较。