A study of an approximation of the non-developable surface and generation of its development

-The method of approximation of the non-developable surface and design of three-dimensional origami using curved folding‐

Abstract

The purpose of this research lies in developing techniques and systems to create actual three-dimensional shape as origami or paper craft. First, we discuss the two curves which presents inherent feature of the surface, called as “zero curve Gaussian curvature curve” and “the extreme curvature curve”, are useful in polygonization of the free-form as a non-developable surface. Then, we discuss a design system of the three-dimensional origami which uses the curved folding. The technique of curved folding makes origami possible to smooth surfaces. And we indicate that shapes can be obtained from the three-dimensional piece of paper with a new curved folding, when you convert a portion of the developable surface reflection across the plane of any developable surface.