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

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Stereographic Draping is a mathematical model of garment draping that unfolds a 3-D garment surface to the corresponding flat garment patterns. This unfolding process is accurate only when the fabric is rigid. In general, it induces distortion in distance and area. The distortion is related to the intrinsic properties of the garment surface and the mechanical properties of the fabric. Mathematically, Stereographic Draping on a general surface is very difficult to be analyzed. Based on representation of the bicubic Bezier patch, the theoretical analysis was conducted to formulate

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Three kinds of cotton fabrics were treated using a practical mercerizing unit under conventional conditions. No change in the lattice type of cellulose was found against the common understanding of mercerization. The reason for this phenomena is thought to be as follows; the mobility of the cellulose molecules in the cotton fabrics is restricted by the construction of the fabrics and the conversion to sodium cellulose as well as conversion from sodium cellulose to cellulose _are hindered. Other physical properties though, were obviously changed by the mercerization. The pore volume increased, water retention decreased, moisture absorbency increased, wet crease recovery increased, dye uptake increased and the bending repulsion increased. In the case of a combination with liquid ammonia treatment, the changes in the water retention, moisture absorbency and crease recovery were enhanced; the pore volume decreased and the changes in the dye uptake and bending repulsion were reduced. Therefore, the combination of mercerization and liquid ammonia treatment should be used depending on the required purpose of the finishing.

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Wetting characteristics of cellulosic substrates designed by partially imitating sized paper surfaces were investigated with regard to the surface morphology by contact angle measurement, atomic force microscopy (AFM) and X-ray photoelectron spectroscopy. The contact angles of water droplets on cellulose films decreased with increasing surface roughness at the nm level according to Wenzel's theory. Binary alkanethiolate self-assembled monolayer (SAM) prepared as a hydrophobic surface model of size components demonstrated the characteristic water repellency of Cassie's theory. These two surface-design methods were combined to control the surface morphology of sized cellulose imitations. Vaporized Au colloids were deposited on the cellulose film, and subsequently dodecanethiol (DT) self-assembled only at the Au positions. The AFM phase images confirmed that the total Au coverage was less than 20% of the substrate surface, but the water repellency of the model cellulosic surface attained ca. 103 deg, which is almost as high as that of the DT-SAM surface (ca. 112deg). These results strongly suggest that the surface morphology involved both in substrate roughness and size distribution must be an important factor in the sizing enhancement, and a good sizing response appears without complete coverage of the hydrophilic substrates by the hydrophobic size components.

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