Conformal Transformation and Application to Origami Designing (New Method to Generate Crease Patterns of Foldable Circular Membranes)

Abstract

This paper presents a new method using conformal transformation to obtain crease patterns of foldable circular membranes by wrapping around a center. This method enables to design complex structures systematically and efficiently from simple structures, controlling angles among fold lines for maintaining significant advantages of origami foldable and developable at will. It is shown that not only existing designs of foldable circular membranes, which are wrapped up and shaped as regular polygons, and also new designs, which are shaped as polygons with different sides or angles like a rectangle or a diamond shape, are successfully produced by the method. For foldable membranes to radial direction, the new method is more flexible to the designing of zigzag fold lines than the previous method by mirror image, since zigzag fold lines can be generated close to the center of membranes without geometrical constraint. Properties of the produced membranes are discussed in the paper.