Computational Generation and Conformal Fabrication of Woven Fabric Structures by Harmonic Foliation

We present a framework for computational generation and conformal fabrication of woven thin-shell structures with arbitrary topology based on the foliation theory which decomposes a surface into a group of parallel leaves. By solving graph-valued harmonic maps on the input surface, we construct two sets of harmonic foliations perpendicular to each other. The warp and weft threads are created afterward and then manually woven to reconstruct the surface. The proposed computational method guarantees the smoothness of the foliation and the orthogonality between each pair of leaves from different foliations. Moreover, it minimizes the number of singularities to theoretical lower bound and produces the tensor product structure as globally as possible. This method is ideal for the physical realization of woven surface structures on a variety of applications, including wearable electronics, sheet metal craft, architectural designs, and conformal woven composite parts in the automotive and aircraft industries. The performance of the proposed method is demonstrated through the computational generation and physical fabrication of several free-form thin-shell structures.

Representative publications:

Journal:

Yang Guo, Qian Ye, Xiaopeng Zheng, Shikui Chen, Na Lei, Yuanqi Zhang, Xianfeng Gu, "Computational Generation and Conformal Fabrication of Woven Fabric Structures by Harmonic Foliation", Computer Methods in Applied Mechanics and Engineering, 363(2020),112874.

Conference:

Yang Guo, Qian Ye, Na Lei, Shikui Chen and Xianfeng Gu, "Fabrication by Foliation", The Shape Modeling International (SMI 2018) Symposium, June 6-8, 2018, Lisbon, Portugal.

Weaving High Curvature Variation Surfaces

Weaving with Different Styles

The Pipeline of Weaving a Genus 2 Surface

Left to right: Computation of two orthogonal harmonic foliations (red loops andblue curves). The red (blue) foliations are converted to white (black) strips. The blackand white strips are woven together to construct the human hand model

Computational Generation of Weaving Stripes on Surface

Conformal Fabrication Steps

Left to right: Conformal fabrication of the genus two model with different weave styles. By adhering all vertical threads under horizontal threads at each paired unit cell, or vice versa, we get a two-layer object, as shown in  (a) and (b). Subfigure (c) is the most common plain weaving; each warp thread passes up-and-down each weft thread.  (d) shows the typical two by two twill pattern, which is done by interlacing the warp thread over two weft threads and then under two weft threads.

(a)

(b)

(d)

(c)