Computational Origami Project

Background

In the summer of 2002, I and Hidekazu Takahashi started a project of Computational Origami. I have been interested in origami since my boyhood. My interest in origami is revitalized by many interesting research results by mathematicians and computer scientists around the end of 1980s. The talk of Corrado Boehm, at IFIP 1.6 WG meeting in Utrecht, 2001, who suggested the implementation of his set of origami axioms, was the start of my actual research of computational origami.

The real progress started when I met Hidekazu Takahashi at ACA conference in@Volos, Greece in the summer of 2002. After we returned to Japan, we met in Tsukuba and designed the basic framework of the origami system. Then, we started to build the computational origami system in Mathematica.

Objectives

Computational origami is to create origami by means of computation. Namely, given a set of formulas obtained by observing geometric properties of origami, by repeated transformation of them, we derive new set of formulas that describe new origami.

Mathematical and Art Origami

Although some origamists are interested in both artistic and mathematical aspects of origami, there are quite separate research issues involved. We are interested in both aspects of origami, but as a research strategy, we separate them and pursue two different goals.

Art Origami

Before describing the theories behind origami creation, let us look at the following examples. They are computed by our system. It is created purely by means of computation of geometric objects associated with origami, i.e. polygons, lines and points, which are rigorously defined in terms of equations.

Instead of showing each steps of origami construction, we put together the origami steps and make them animate. We plan to have a rich collection of origami art pieces At this moment, we need to supply parameters in mathematical forms in order to instruct the system to make a fold of origami. We plan to make an interface to facilitate the input of parameters for folding.

Mathematical Origami

This is our attempt to provide a web-based interface to mathematically motivated origamists. Please visit our web@site.