Complete and robust no-fit polygon generation for the irregular stock cutting problem

The no-fit polygon is a construct that can be used between pairs of shapes for fast and efficient handling of geometry within irregular two-dimensional stock cutting problems. Previously, the no-fit polygon (NFP) has not been widely applied because of the perception that it is difficult to implement and because of the lack of generic approaches that can cope with all problem cases without specific case-by-case handling. This paper introduces a robust orbital method for the creation of no-fit polygons which does not suffer from the typical problem cases found in the other approaches from the literature. Furthermore, the algorithm only involves two simple geometric stages so it is easily understood and implemented. We demonstrate how the approach handles known degenerate cases such as holes, interlocking concavities and jigsaw type pieces and we give generation times for 32 irregular packing benchmark problems from the literature, including real world datasets, to allow further comparison with existing and future approaches.