A Method of Predicting Sewn Shapes by Polyhedrons

Abstract

To make 2D patterns of a garment, it must be noted that there are two types of parts. Some are flexible parts, for example drape in skirts, and others are stiff parts, for example collars. It is difficult to estimate the 3D form after sewing with 2D patterns in flexible parts. On the other hand, it is not so difficult to estimate that in stiff parts. Here, we focus on design of the stiff parts. We assumed that garments are made of paper, and have already predicted a continuous 3D form of a garment by using the theory of developable surfaces. Solutions were, however, usually differential equations these were not integrable. It was not general-purpose system. The aim of this paper is to make a general-purpose system for predicting the 3D form of garments after sewing. We approximate sewn curves to polygons, and seek the 3D form of garments after sewing and feasible region on the 2D patterns by using polyhedrons. At the same time, we considered the difference between the continuous system and proposed discrete system.
We made the general-purpose prototype system by using an example, regular n th pyramid. As for the differences between the continuous system and the discrete system, the following three results were obtained. (1) Users can set up a first standing angle of regular n th pyramid. (2) The larger a difference between a standing angle corresponded with continuous system and a first standing angle become, the shorter a length of generating lines are. (3) The higher the accuracy of approximation becomes, the bigger the influence that the difference between the two angles gives the length of generating line is.