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 three-dimensional 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.

我们开发了一种基于优化的方法来模拟缩褶，这是一种表面刺绣技术，可提供装饰性几何纹理，同时保持织物的拉伸性能。在缩褶过程中，织物上的多对点被缝合在一起，形成非流形的几何特征和视觉上令人愉悦的纹理。设计抽褶图案具有挑战性，因为缝合的结果是不可预测的：最终的纹理通常只有在整个抽褶过程完成后才会显现出来，这需要艰苦的物理制造和耗时的试错实验。这促使我们寻求一种数字化的抽褶设计方法。使用表面变形或布料模拟​​方法来计算缩褶织物几何形状的直接尝试未能产生真实的结果，这可能是由于设计结构复杂、接触数量大和高曲率折叠。相反，我们将缩褶表述为图形嵌入和形状变形问题。我们提取代表织物和缝合约束的粗图，然后导出缩褶结果的图结构。我们解决了该图的三维嵌入问题，从而可靠地引导了高分辨率织物网格的变形。我们基于优化的方法简单、高效、灵活，这使我们能够构建一个用于褶皱图案探索的交互式系统。为了证明我们方法的准确性，我们将我们的结果与大量缩褶图案的真实制作结果进行比较。