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Development of algorithms for the formation and placement of N-dimensional orthogonal polyhedrons into containers of complex geometric shape

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Abstract

The article is devoted to problems related with the development of algorithms for creating, optimizing and placing of orthogonal polyhedrons of arbitrary dimension. Under N-dimensional orthogonal polyhedron is understood a composite object represented as a set of N-dimensional parallelepipeds with a fixed position relative to each other, which is considered as a whole. The need to solve the problem of placing a set of objects in the form of orthogonal polyhedrons of arbitrary dimension arises when solving a large number of practical problems in the automation of design and production. In particular, solving the layout problems of equipment and space, problems of cutting materials, problems of designing very large-scale integrated circuits, and optimizing the distribution of resources in computing and production systems, as well as many other actual problems, can be reduced to solving the problem of packing orthogonal polyhedrons. To create a new N-dimensional orthogonal polyhedron, the operations of addition, subtraction and multiplication of orthogonal objects are implemented. With the aim to increase the placement speed of orthogonal polyhedrons which were created with using the voxel model, an algorithm for partitioning of an orthogonal polyhedron into many non-overlapping each other as large as possible large orthogonal objects is proposed. In the scientific literature, there are no solutions to the problem of partitioning an orthogonal polyhedron of arbitrary dimension. The proposed partitioning algorithm is based on the usage of a model of potential containers developed to solve the orthogonal packing problems of arbitrary dimension. To obtain a container of arbitrary shape, a possibility of setting its geometric constraints with an orthogonal polyhedron is implemented. The article presents an algorithm developed for packing an N-dimensional orthogonal polyhedrons inside containers of arbitrary geometric shape, based on the application of multiplication orthogonal polyhedrons operations to obtain the set of points of permissible placement of each considered object. The examples of solving the problems of cutting the industrial materials into objects of irregular shapes, as well as solving the problems of placement complex objects created with using the voxel model into containers of various geometric shapes (including sphere and cone) are given. The effectiveness of the application of the developed algorithms is shown on the example of solving the problem of generation a dense layout of details on a 3D printer platform.

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Availability of Data and Material (data transparency)

All data and materials are given in this article.

Code Availability (software application or custom code)

The source code of the software that implements the developed algorithms is not publicly available anywhere.

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  1. Vladislav A. Chekanin & Alexander V. Chekanin

    Present address: Moscow State University of Technology “STANKIN”, 3a Vadkovsky lane, Moscow, 127055, Russia

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    Chekanin, V.A., Chekanin, A.V. Development of algorithms for the formation and placement of N-dimensional orthogonal polyhedrons into containers of complex geometric shape. Int J Adv Manuf Technol 117, 2467–2479 (2021). https://doi.org/10.1007/s00170-021-06974-y

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