Pattern development involves mapping 3D surfaces into 2D flat patterns. To reduce the complexity of patterns, approximations of the surfaces into polygonal surfaces such as quadrilateral or triangular facets are usually necessary. This paper is concerned with the pattern development of polygonal surfaces with a special reference to bent sheet metal parts. The development process needs to consider the unfoldability of 2D patterns. The unfoldability requires that the 2D pattern does not overlap itself, and the faces of the part do not distort during bending. For some designs, there are multiple 2D patterns that can all be bent into the same 3D shape. The compact pattern is usually selected due to better stock utilization in cutting and nesting and ease of handling during bending. We show that the development of the compact 2D pattern can be converted into a minimum cost spanning tree problem. This approach has been implemented using an A* search algorithm and several examples are presented.
C.-H. Wang and D. A. Bourne, ``Compact 2D Pattern Development from 3D Polygonal Surfaces,'' ASME Design for Manufacturing Conference (ASME96-DETC), Irvine, 1996.