Constructing of $OE$-postman path for a planar graph

The model of cutting plan can be presented as a planar graph for automated system of sheet material cutting process preparation. The aim of such modelling is a definition of the shortest path of a cutter having no parts requiring any additional cuttings. The paper is devoted to a problem of chines postman path constructing for a planar graph representing a cutting plan. This path has a restriction of ordered enclosing (i.e. cycle of passed edges does not contain inside not passed ones). The path satisfying this restriction is also called $OE$-path. This kind of restriction means the lack of additional cuttings of details. The recursive algorithm for constructing of this type of paths is considered in the paper. It is proved that this algorithm has a polynomial complexity. The developed software allows to solve the problem for an arbitrary planar graph. The software is tested for the typical cases of planar graphs.