Abstract
In this paper, a new technique is shown to obtain developed patterns of conical shells and circular membranes from ones of cylinders by using the conformal transformation. It enables to design foldable structures systematically, controlling angles among fold lines for maintaining advanced functions particular to origami such as foldability, expandability, inflatability and so on. Also, it is able to yield new saddle-shaped structures based on fluid flows. It is described the mathematical interrelation of developed patterns between cylinders and conical shells, and advantages on applying the mathematical technique on designs of origami structures. The method is to help us to imagine and model new shapes of structures for future application on engineering.
