Continuous deformation of flat-foldable crease patterns via interpretation as set of twist-patterns

Abstract

In the study of origami, various parametric methods have been proposed to design crease patterns under geometric conditions for flat-folding. Each design method contributes to finding a desirable crease pattern, e.g., one with superior engineering properties, by manipulating parameters. On the other hand, to continuously deform other crease patterns, it is necessary to recreate it once with such a parametric method; however, this inverse problem is less studied. This paper is basic research to solve this problem and to allow parametric deformation of flat-foldable crease patterns. Given crease patterns are interpreted as networks consisting of twist-folding patterns that can be generated by an existing parametric method named Twist-based design method. Then, by manipulating the parameters, the crease pattern is deformed. Importantly, any flat-foldable crease pattern having no crease line connecting two points on the boundary can be targeted, and it is locally guaranteed that deformed crease patterns have non-intersecting crease lines and are flat-foldable. The proposed method contributes to increased origami variations by deformations of existing crease patterns.