Fig. 3: Quantifying the correlation between the boundary curvature and the Gaussian curvature.
From: Boundary curvature guided programmable shape-morphing kirigami sheets
a, b Theoretically predicted 3D maps of the normalized Gaussian curvature \(\bar{K}\) at the center point C as a function of the normalized boundary curvature \({\bar{k}}_{{{{{{\mathrm{bo}}}}}}}\) in 2D kirigami precursors (insets) and the applied strain ε for the cases of spherical (a) and saddle (b) shapes. The color bars represent the normalized Gaussian curvature. c Theoretical and experimental results of the approximately linear relationship between the normalized variation of the Gaussian curvature \(|\varDelta \bar{K}/{\bar{K}}_{\max }|\) and the normalized variation of the boundary curvature \(|\varDelta {\bar{k}}_{{{{{{\mathrm{b}}}}}}}/{\bar{k}}_{{{{{{\mathrm{bo}}}}}}}|\).
