Distortion Theory of Stereographic Draping with Flexible Fabric on Surface of Constant Curvature

Abstract

The 3-D to 2-D surface unfolding problem is known as draping in the apparel industry. In practice, draping involves distance and area distortion, but the quest of a systematic method to calculate the distortion has not been satisfied. Stereographic Draping (SD) is used to derive the distortion property with respect to the surface of constant curvature. In the Stereographic Draping, the position of a point, s, on a 3-D garment surface is mapped to the image, q, on the 2-D flat pattern based on the calculation of the distance of s with respect to two reference points available on the flat pattern. Generally, the fitting of the flexible fabric on a surface depends on the intrinsic structure of the surface and mechanical properties of the fabric. Correspondingly the Stereographic Draping composes of two components. Since the deformed state is effectively a change in the position on the surface patch with respect to the relaxed state, the unfolding map is a composite function of the geometric component and the mechanical component. In this article, the theoretical analysis provides the distortion properties on distance and area when direct measurement and positioning from the garment surface of constant curvature is transferred to the flat pattern.