articles

The article presents the developed packing algorithms that make it possible to solve the problem of optimized placement of a given set of flat objects taking into account additional geometric and technological constraints specified when arranging real objects in production. A description of the procedure for applying individual indents between object boundaries is given. To work with areas of placement of arbitrary geometry, restricted areas in the form of fixed objects of various geometries are introduced. An algorithm for uniform placement of a given set of objects throughout the given placement space is proposed. An algorithm for placing objects taking into account several placement start points is described, ensuring their placement as close as possible to one or two pre-marked points in the placement space. A speed-optimized algorithm for placing flat objects of arbitrary geometry, presented in the form of orthogonal polyhedra, is proposed, implementing fast layout of objects of complex geometry when arranging taking into account specified indents and placement start points. An algorithm for arranging flat objects is developed taking into account individual constraints on the minimum distance between special points of objects. A heuristic algorithm for selecting the best variant of orthogonal orientation of rectangular objects is proposed, minimizing the density of the formed layout. Examples of various layouts of objects obtained using the developed placement algorithms are given. Examples of solving some particular problems of arranging rectangular objects with various restrictions on the minimum distance specified between special points of objects are presented. The use of developed packing algorithms, taking into account various geometric and technological limitations, makes it possible to solve practical problems of arranging objects in real production conditions.