Distortion-minimizing surface parameterization is an essential step for computing 2D pieces necessary to fabricate a target 3D shape from flat material. Garment design and textile fabrication are a prominent application example. Common distortion measures quantify length, angle or area preservation in an isotropic manner, so that when applied to woven textile fabrication, they implicitly assume fabric behaves like paper, which is inextensible in all directions and does not permit shearing. However, woven fabric differs significantly from paper: it exhibits anisotropy along the yarn directions and allows for some degree of shearing. We propose a novel distortion energy based on Chebyshev nets that anisotropically penalizes shearing and stretching. Our energy formulation can be used as an optimization objective for surface parameterization and is simple to minimize via a local-global algorithm. We demonstrate its advantages in modeling nets or woven fabric behavior over the commonly used isotropic distortion energies.

中文翻译：

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机织织物建模的 Chebyshev 参数化


最小化失真的表面参数化是计算从平面材料制造目标 3D 形状所需的 2D 工件的重要步骤。服装设计和纺织品制造是一个突出的应用示例。常见的变形测量以各向同性方式量化长度、角度或面积保持，因此当应用于机织纺织品制造时，它们隐含地假设织物的行为类似于纸张，纸张在所有方向上都不可拉伸，并且不允许剪切。然而，机织织物与纸张有很大不同：它沿纱线方向表现出各向异性并允许一定程度的剪切。我们提出了一种基于切比雪夫网的新型畸变能，它对剪切和拉伸进行各向异性惩罚。我们的能量公式可以用作表面参数化的优化目标，并且很容易通过局部-全局算法最小化。我们展示了它在模拟网络或机织织物行为方面相对于常用的各向同性畸变能量的优势。