An Overview of Methods to Form Orthogonal Polyhedra for the Problems of Packing Objects of Complex Shape

Abstract

The article is devoted to the analysis and systematization of methods that ensure the formation of orthogonal polyhedra of arbitrary dimension for the discrete representation of objects and containers of complex shape in cutting and packing problems. Methods of creating orthogonal polyhedra based on a number of set-theoretic operations (addition, subtraction and intersection operations), analytical formation using a set of functions and relation operations, as well as voxelization of flat and volumetric models are considered. The method based on set-theoretic operations is intended primarily for the manual creation of new orthogonal polyhedra characterized by relatively simple geometry. The method of analytical formation is best used to create orthogonal polyhedra whose shape can be parametrically described. The voxelization method is universal, it is used to form orthogonal polyhedra based on vector models of arbitrary geometry. An algorithm for creating a container in the form of an orthogonal polyhedron based on a given vector model is proposed, which makes it possible to solve the problem of packing objects inside a container of arbitrary geometry. An example of solving the problem of packing objects of complex geometry represented by orthogonal polyhedra inside an irregular container is presented.