Fig. 3.

Schematic to provide intuition for the three projection terms K, S, and I Simulations of basic folded ribbons as sinusoidal oscillations on a circle. In this shape we can change the overall radius of the encapsulating circle ($A_e$), the thickness ($T$) encapsulated by the outer and inner oscillations (dark and light blue), and the amplitude of the oscillations, which dictate the total length of the oscillation ($A_t$). By scanning the radius, thickness, and oscillation amplitude in a 3D space, we can calculate the corresponding value for the $K,$$S,$ and $I$ term at different points in this space (colour map). Transparent arrows point in the directions of change of $K,$$S,$ and $I$. Through visualising the changes in $K,$$S,$ and $I$ in this 3D space, we provide an intuition for how the three terms relate to parameters in a simple folded structure.