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 produce nonzero Gaussian curvature, albeit with faceted surfaces. We demonstrate that, by tuning the in-plane curvature of ribbons, integrated weave can be varied continuously, which not feasible traditional techniques. Further, we reveal shape physical unit cells dictated solely geometry elasticity. Finally, leverage geometry-driven nature triaxial design set ribbon profiles smooth spherical, ellipsoidal, toroidal structures.