A new technique for nesting irregular shapes based on rectangular modules

Abstract

A common problem often faced by designers in the shipbuilding, clothing, or leather manufacturing industries is nesting irregular (nonrectangular) shapes into rectangular sheets. The basic goal is to achieve a good layout that minimizes the total material wastage. This problem is difficult to formulate and there are no known approaches that directly use any mathematical model. The nesting problem is usually tackled by heuristic approaches. This chapter describes the design and development of heuristic technique for solving the nesting problems into clear/defective sheets. The suggested solution technique is based on three computer graphics routines, namely, interactive graphics routine to define the shape and the clustering pattern, rectangular graphics routine to compute the best rectangular modules that completely encloses the defined shapes and/or clustering patterns, and automatic layout graphics routine for nesting the computed rectangular modules and correspondingly the original shapes. Each of these three routines is described by an illustrative example. The feature of applying the developed nesting technique for defective sheets is also presented. In addition, the results obtained when the technique installed to some nesting problems are discussed.