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Triaxial weaving is a handicraft technique that has long been used to createcurved structures using initially straight and flat ribbons. Weavers typicallyintroduce discrete topological defects to produce nonzero Gaussian curvature,albeit with faceted surfaces. We demonstrate that, by tuning the in-planecurvature of the ribbons, the integrated Gaussian curvature of the weave can bevaried continuously, which is not feasible using traditional techniques.Further, we reveal that the shape of the physical unit cells is dictated solelyby the in-plane geometry of the ribbons, not elasticity. Finally, we leveragethe geometry-driven nature of triaxial weaving to design a set of ribbonprofiles to weave smooth spherical, ellipsoidal, and toroidal structures.

Smooth triaxial weaving with naturally curved ribbons