Geometry Workshop Obergurgl 2021

Basket weaving is a traditional craft of interlacing flexible straight ribbons to create curved structures. One method for injecting curvatures in a straight-ribbon weave is to place topological singularities in the regular weaving pattern. However, topological singularities often result in curvature concentrations since they are inherently discrete. Determining where to place the singularities are also non-trivial. We propose an optimization-based approach to construct smooth free-form woven surfaces using curved ribbons. Our algorithm accurately tracks the elastic behaviors of the interlaced ribbon assembly and computes the best planar geometry for each ribbon to closely approximate a given target design surface. With the additional ribbon curvature degrees of freedom and an efficient physics-based optimization framework, we are able to produce a broad range of previously impossible woven shapes. We validate our approach by comparing the 3D scan of physical prototypes with simulation results.