Smooth Triaxial Weaving with Naturally Curved Ribbons

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.

Automated summary

The technique of triaxial weaving involves creating curved structures using initially straight ribbons and tuning the in-plane curvature to vary the Gaussian curvature continuously. The shape of the physical unit cells is determined by the in-plane geometry of the ribbons, rather than elasticity. By leveraging the geometry-driven nature of triaxial weaving, smooth spherical, ellipsoidal, and toroidal structures can be designed.