This research studies some issues related to approximate surface development. Two related problems are also explored as described below. The main work here is the development of an iterative algorithm for generating 2D 'flattened’ patterns equivalent to a 3D shape that possibly has non-zero Gaussian curvature. The equivalence here is meant in terms of minimization of the strain energy. The model used incorporates approximated solid mechanics to compute the strain and the strain energy of the surface. The principal strain directions are used to guide the flattening algorithm. The method yields some advantages over the ones reported in recent research since it uses a more accurate energy model, and searches for energy minimization over a continuous domain (instead of taking discrete steps...[ Read more ]

This research studies some issues related to approximate surface development. Two related problems are also explored as described below. The main work here is the development of an iterative algorithm for generating 2D 'flattened’ patterns equivalent to a 3D shape that possibly has non-zero Gaussian curvature. The equivalence here is meant in terms of minimization of the strain energy. The model used incorporates approximated solid mechanics to compute the strain and the strain energy of the surface. The principal strain directions are used to guide the flattening algorithm. The method yields some advantages over the ones reported in recent research since it uses a more accurate energy model, and searches for energy minimization over a continuous domain (instead of taking discrete steps). We also explore how to arrange a developed pattern onto a raw stock (sheet) of anisotropic properties, so as to minimize the strain energy. This has applications in engineering where raw material patterns are cut out of flat stocks, and then 'draped’ or forced on top of moulds to form curved surfaces, as in footwear manufacturing. The second problem we study is the draping of a 2D pattern of polygonal shape onto a given 3D curved surface. A new method using geodesic curves is explored for this problem. A major difference between the methods of this work with many of the past works is that we do not allow any darts or gussets in the developments. This is consistent with our major application area, which is footwear design. The techniques developed in this research have direct application in this industry, which is an important sector in Hong Kong manufacturing -- HK is the third largest exporter of leather goods in the world.