Irregular Packing Using the Line and Arc No-Fit Polygon

The no-fit polygon is a geometric construct that can offer faster and more efficient handling of geometry between pairs of shapes than traditional line-by-line intersection. The detection of intersections is a critical operation within the irregular two-dimensional stock-cutting problem (also known as “nesting”), which aims to place shapes onto sheets of material so that the material is utilised as efficiently as possible and the waste (or trim loss) is reduced. The problem forms an important process within many real-world manufacturing industries such as metalworking, automotive production, aerospace, clothing and conservatory manufacture, and others. If manufacturers can reduce their costs by utilising raw materials more effectively, this can directly translate into increased profit margins or greater competitiveness within the marketplace. Moreover, there are significant environmental benefits to be gained. Several methods have been proposed to calculate no-fit polygons, but most, if not all, can only operate on geometry that consists of line segments. This paper extends the orbital sliding method of calculating no-fit polygons to enable it to handle arcs and then shows the resultant no-fit polygons being utilised successfully on the two-dimensional irregular packing problem. As far as the authors are aware, this is the first time that a no-fit polygon algorithm has been able to handle arcs robustly without decomposing to their line approximations. The modification of the authors' previously published packing algorithm to utilise the proposed no-fit polygon approach yields solutions of excellent quality (including several best-known) on well-established literature benchmark problems after only a few minutes. The authors believe that the success of the packing strategy and the line and arc no-fit polygon algorithm make this approach a serious candidate for use in real-world production environments.