Abstract
Abstract Lots of studies on tool paths for cutting machines mainly deal with contour by contour cutting. While constructing a path one needs to determine the pierce point and the direction of contour passing. In this case only the length of idle passes may be optimized. To solve this problem generalized travelling salesman problem (GTSP) approach is used. Resource-efficient technologies for cutting sheet materials allow for the contours of cut-off details to be overlapped. It allows reducing the material waste and shortening the length of cuts. Common cuts are also the origin of one more set of precedence constraints. These constraints can be formalized as one general formal restriction called as Ordered Enclosing (OE) for plane graphs that are the homeomorphic images of the cutting plan. In this report we consider the common case of a cutting problem when combination of contours is allowed. We review the polynomial algorithms for all the possible restrictions: (1) part cut off a sheet does not require further cuts (constructing of OE-route); (2) there are no intersections of cuts (constructing of NOE-route); (3) there are some restrictions on placement of pierce points (constructing of PPOE-cover). Our paper considers software that, according to the cutting plan, allows to get a homeomorphic image of the graph to solve the routing problem, solves this problem and interprets the results of the solution.
Published Version
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