平滑三轴编织与自然弯曲的丝带
Smooth triaxial weaving with naturally curved ribbons
摘要：
三轴编织是一种手工艺技术，长期以来一直用于使用最初的直线和平面带状物创建弯曲结构。织工通常引入离散拓扑缺陷来产生非零高斯曲率，尽管是小面的表面。我们证明，通过调整的平面内的带状物的曲率，积分高斯曲率的编织可以连续变化，这是不可行的，使用传统的技术。此外，我们揭示了物理单位单元的形状仅由带状物的平面内几何形状决定，而不是弹性。最后，我们利用几何驱动的三轴编织的性质来设计一组带状轮廓编织光滑的球形，椭球形和环形结构。
英文摘要：
Triaxial weaving is a handicraft technique that has long been used to create curved structures using initially straight and flat ribbons. Weavers typically introduce discrete topological defects to produce nonzero Gaussian curvature, albeit with faceted surfaces. We demonstrate that, by tuning the in-plane curvature of the ribbons, the integrated Gaussian curvature of the weave can be varied continuously, which is not feasible using traditional techniques. Further, we reveal that the shape of the physical unit cells is dictated solely by the in-plane geometry of the ribbons, not elasticity. Finally, we leverage the geometry-driven nature of triaxial weaving to design a set of ribbon profiles to weave smooth spherical, ellipsoidal, and toroidal structures.
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