A modeling method of curved folding considering ruling intersection

Abstract

Curved folding is a way of folding a sheet of paper along a curved crease. By using curved foldingƅone can make beautiful shapes which have curves and curved surfaces. A shape created by curved folding is composed by straight lines called ruling. Because this ruling has an important property that they do not intersect on a sheet of paper, existing system to design curved folding requires users to avoid this intersection manually. In this paper, we introduce a method to avoid intersection of rulings automatically. We define an objective function that outputs degree of intersection and a penalty function which keeps the shape from large deformation. By solving these functions as an optimization problem, we implemented a system which helps us to design curved folding more quickly and easily