Mathematical elucidation of the traditional Japanese fan focusing on its structure

The Japanese traditional fan, which is a form of origami originating in Japan with a folding culture, has a variety of three-dimensional expression that differs from two-dimensional expression. The image painted on the fan deforms when the fan is folded. In this study, we create a digital fan model for clarifying the deformation on the fan face according to parameters such as length of the bamboo bones. We then validate the digital model with an actual fan. Furthermore, we obtain the original plan view from images of the folded fan as a reverse problem. Because folding fans are made of paper and bamboo and held in the hand, old traditional folding fans are more or less damaged; for example, many culturally valuable folding fans have lost their bones and have damaged edges, have been stretched flat, and have been framed like paintings. Reproducing the original fan without information of the original form is difficult. In the present study, we provide a digital fan model for examining the original fan shape. Old valuable folding fans are treasured by museums and collectors around the world. In future research, we would like to capture such precious folding fans in three-dimensional space applying our digital fan model and to exhibit these fans in a digital museum, providing opportunities not only to enjoy the value of the fans but also to encourage the research of Japanese traditional culture.