Geometrical optimization of weaving paper strips for a general curved surface

Abstract

Paper sheet is a kind of soft material with high flexibility compared to the bulk counterpart. The flexibility comes from the geometry of thin shape, rather than the mechanical properties of the material itself. In this study, we develop a method of constructing curved surfaces using the flexible deformation of paper sheet. The target surface is divided into several pieces using space curves which are characterized as a straight line on a parameter space. The geodesic curvature, which is the projection of the normal curvature of the space curve onto the tangent plane, is used to approximate the piece of surface on a flat paper. We made several curved surfaces including hemisphere, torus and catenoid.