Fig. 2. Unfolding approach and optimization procedure of the multi-ply stacking.
(A) Schematic of unfolding a polyhedral mesh into a 2D net to conform a prescribed 3D curved surface. (B) Optimization procedure to avoid overlap of cuts at the same location. The cut edges of each ply are mutually exclusive from those of other plies by mutating the weights of the cutting graph. (C) Stacking of four optimized plies without cut overlapping. The existence of cuts is ignored where the tabs are introduced. (D) Comparison of the number of overlapped cuts from the random design and the optimized designs with and without tabs. The colors of lines in the cutting graph indicate different numbers of overlapped cuts. The bar charts illustrate the ratio of the number of overlapped cuts to the total number of edges nedge in the mesh. Each design consists of eight plies.