Conic curved creases with reflected rule lines is a style of curved origami design, first explored by David Huffman, that is attractive in that it gives one-DOF folding motions with rigid rule lines (i.e., the rule lines remain the same throughout the motion). We show how to discretize any such curved crease pattern into a similar straight-line crease pattern that has a one-DOF rigid folding motion. We develop two general methods for such discretization, where each curve is replaced by an inscribing or circumscribing polygonal line, respectively, and show in both cases that the resulting discretized crease patterns are rigidly foldable. In the case of the circumscribed discretization, the crease pattern is also locally flat foldable. On the other hand, only careful sampling in the inscribed method results in locally flat-foldable crease patterns.
Read more in our paper.
We implemented a Grasshopper / Rhino plug-in for experimental design. Here are some further examples.