Column-shaped Origami Design Based on Mirror Reflections

Origami, which is the construction of an object by folding a single sheet of paper, has been studied in the fields of mathematics and engineering. Several software programs for designing origami shapes have been recently developed, and so we can now obtain a variety of shapes. However, the variations designed with them are still limited. In this paper, we propose a new method for designing origami based on the sweep and reflection operations. As an example, a column-shaped origami object with a relief structure is designed using our method. The shape is defined by a profile polyline and a trajectory polyline that are input by the user. We developed a system on which the user inputs and edits the polylines to generate both the crease pattern and the 3DCG model of the origami object in real time. With the tools implemented in our system, the user can design a wider variety of shapes in a trial-and-error manner while seeing the effects of their operations. Thus, users can easily design stable and geometrically attractive shapes. We indicate the effectiveness and the potential of our system by showing some examples.