Distortion Theory of Stereographic Draping with Rigid Fabric

Abstract

Draping, or garment pattern unfolding process, is a 3-D to 2-D surface unfolding problem. In practice, although the pattern designers are aware of the distortion, they do not have any systematic method to calculate the distortion and they do not know how such distortion relates to curvature or other properties. In this article, the mathematical model of Draping, Stereographic Draping (SD), is used to derive the distortion property. In this method, two selected reference points, r0 and r1, on the surface are mapped to p0 and p1 on the plane according to their distance apart. Then the position of a point, s, on a 3-D garment surface is mapped to the corresponding image, q, on the 2-D flat pattern based on the calculation of the distance of s with respect to r0 and r1. It is equivalent to finding the solution of intersection of two circles. In general, such technique involves distortion, because the different garment surfaces have different intrinsic properties, and may not be isometric, or preserve distance. Although fabric properties can affect the fitting of fabric to the mannequin, when the fabric is rigid, such as paper or non-woven fabric, the Draping process is assumed to be unaffected by fabric properties. The scope of the problem can be confined to the geometric analysis. In this article, the theoretical analysis provides the distortion properties of distance and area with the condition when direct measurement and positioning from the developable garment surface can be accurately transferred to the flat pattern.