Abstract
The article is devoted to algorithms developed for solving the problem of placement orthogonal polyhedrons of arbitrary dimension into a container. To describe all free areas of a container of complex geometric shape is applied the developed model of potential containers. Algorithms for constructing orthogonal polyhedrons and their subsequent placement are presented. The decomposition algorithm intended to reduce the number of orthogonal objects forming an orthogonal polyhedron is described in detail. The proposed placement algorithm is based on the application of intersection operations to obtain the areas of permissible placement of each considered object of complex geometric shape. Examples of packing sets of orthogonal polyhedrons and voxelized objects into containers of various geometric shapes are given. The effectiveness of application of all proposed algorithms is presented on an example of solving practical problems of rational placement of objects produced by 3D printing technology. The achieved layouts exceed the results obtained by the Sinter module of the software Materialise Magics both in speed and density.
Highlights
The problem of packing objects of irregular geometric shape has a large number of practical applications in various fields, including cutting of industrial materials, layout of spaces, covering problems, modeling the microstructure of materials, active electronically scanned arrays generation and other relevant problems [1,2,3,4,5]
The developed algorithm for packing orthogonal polyhedrons was applied to solve practical problems of rational placement of objects produced by 3D printing
Using the developed model of potential containers to describe the free spaces inside a container, it is possible to obtain the best area for placing irregular objects inside geometrically complex containers
Summary
The problem of packing objects of irregular geometric shape has a large number of practical applications in various fields, including cutting of industrial materials, layout of spaces (spaces of aircraft, ships and etc.), covering problems, modeling the microstructure of materials, active electronically scanned arrays generation and other relevant problems [1,2,3,4,5]. To solve the problem of packing objects of irregular geometric shape is proposed to present the objects as the orthogonal polyhedrons which combine non-overlapping orthogonal objects (rectangles or parallelepipeds in the twodimensional or three-dimensional case, respectively) with a fixed position relative to each other [17,18,19,20]. This approach makes it possible to solve the problems of packing voxelized objects of complex geometric shape [21, 22].
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