Nihon Kikai Gakkai ronbunshu (May 2021)
Mathematical elucidation of the traditional Japanese fan focusing on its structure
Abstract
Japanese traditional fan has the variety of three-dimensional expression that differs from two-dimensional expression. The image painted on the fan deforms, when it is folded into convex-concave configuration and fixed to the bamboo bones，due to the difference between the shrinking percentage of the outer arc and the inner arc. Many of the fans made until the Edo era are thought to be painted in consideration of the deformation, but this idea is not recognized in the field of traditional Japanese art. Therefore, many culturally valuable fans, which are more or less damaged due to aging, have lost their bones and damaged edges, and stretched flat like paintings. The fan surface is preserved but the original value of the fan is lost. In this study, we create a digital fan model by proposing approximate formulas for clarifying the deformation on the fan face according to parameters such as length of the bamboo bones, to support the opinion that three-dimensional configuration is essential for folding fans. We then validate the digital model with an actual fan. Regarding shape and area, there was good results, although further study is necessary to improve it. Furthermore, we obtain the original plan view from images of the folded fan as a reverse problem, which is useful for product development that makes use of the characteristics of folding fans.In future study, we would like to upgrade this model to the tool that assists the difficult task of reproducing folding fan without its original configuration. Also we would like to capture precious folding fans in three-dimensional space applying this model and to exhibit those fans in a digital museum, to give opportunities not only to enjoy the value of them but also to encourage the research of the Japanese traditional culture.
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