The geometry of nesting problems: A tutorial

Cutting and packing problems involving irregular shapes is an important problem variant with a wide variety of industrial applications. Despite its relevance to industry, research publications are relatively low when compared to other cutting and packing problems. One explanation offered is the perceived difficulty and substantial time investment of developing a geometric tool box to assess computer generated solutions. In this paper we set out to provide a tutorial covering the core geometric methodologies currently employed by researchers in cutting and packing of irregular shapes. The paper is not designed to be an exhaustive survey of the literature but instead will draw on the literature to illustrate the theory and implementation of the approaches. We aim to provide a sufficiently instructive description to equip new and current researchers in the area to select the most appropriate methodology for their needs.