Construction of 3-D Virtual Origami Models from Sketches

A modern technique of designing origami has been established for several decades. This technique enables people to constitute a crease pattern by drawing lines (creases) on a sheet of paper based on mathematical theories, and to create realistic origami works. However, design of the crease patterns using this technique requires expertise. Furthermore, it is difficult to fold the origami model from the designed crease pattern. To solve these problems, we develop a system that automatically designs crease patterns from images of figures such as handwritten sketches, and constructs the paper-made objects by computer graphics techniques. Even if there is no information that tells how to fold the object users want, origami models can be constituted from some images users input. It becomes possible to constitute origami models which users intend at any time. Figure 1 shows the processing flow of our system proposed in this paper. We firstly propose a method that analyzes images based on symmetry. We assume that users draw symmetrical objects such as animals onto the images. By using this method, symmetrical structures of thinned diagrams extracted from the images are recognized. Secondly, we describe a method for constituting crease patterns based on general origami design methods. Thirdly, a method for constructing a 3-D paper-made object from the crease pattern is proposed. This method first transforms 2-D coordinates of origami models into 3-D ones. Since faces (formed by creases) more than two are likely transformed onto the same plane in 3-D models, it is necessary to dispose these faces consistently. Therefore, second, a method for analyzing positional relationships of the overlapping faces is proposed. To show the validity of proposed method and algorithm, we finally demonstrate how a crease pattern is generated and how an origami model is actually constructed based on sketches and object skeletons extracted from images.