Efficient algorithms for orthogonal packing problems

Chekanin, Alexander V.; Chekanin, Vladislav A.

doi:10.1134/s0965542513100047

Cited by 14 publications

(16 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To describe a packing entire is used the developed model of potential containers [20,21]. A potential container is an imaginary orthogonal region ( D -dimensional parallelepiped) for which there is free space inside a packing.…”

Section: Developed Algorithms For Working With Orthogonal Polyhedrons 21 Description Of Container Free Spacesmentioning

confidence: 99%

See 1 more Smart Citation

Algorithms for Working with Orthogonal Polyhedrons in Solving Cutting and Packing Problems

Chekanin

2021

Proceedings of the 31th International Conference on Computer Graphics and Vision. Volume 2

View full text Add to dashboard Cite

In this paper problems of cutting and packing objects of complex geometric shapes are considered. To solve these NP-hard problems, it is proposed to use an approach based on geometric transformation of polygonal objects to composite objects (orthogonal polyhedrons) made up of rectangles or parallelepipeds of a given dimension. To describe the free space inside a voxelized container, a model of potential containers is used as the basic model that provides the ability of packing orthogonal polyhedrons. A number of specialized algorithms are developed to work with orthogonal polyhedrons including: algorithms for placing and removing composite objects, an algorithm for forming a packing with a given distance between objects to be placed. Two algorithms for the placement of orthogonal polyhedrons are developed and their efficiency is investigated. An algorithm for obtaining a container of complex shape presented as an orthogonal polyhedron based on a polygonal model is given. The article contains examples of placement schemes obtained by the developed algorithms for solving problems of packing two-dimensional and three-dimensional non-rectangular composite objects.

show abstract

Section: Developed Algorithms For Working With Orthogonal Polyhedrons 21 Description Of Container Free Spacesmentioning

confidence: 99%

“…of the considered orthogonal polyhedron. When all compound objects consist of only one simple object, then the problem is reduced to the classical problem of orthogonal packing or rectangular cutting [2,20].…”

mentioning

confidence: 99%

Algorithms for Working with Orthogonal Polyhedrons in Solving Cutting and Packing Problems

Chekanin

2021

Proceedings of the 31th International Conference on Computer Graphics and Vision. Volume 2

View full text Add to dashboard Cite

show abstract

“…The problem of packing objects of complex geometric shape has a large number of practical applications in various areas. Solving the problems of cutting industrial materials, rational usage of free spaces (for example, ships or aircraft), geometric surface coverage with specified shapes, modelling the microstructure of composite materials as well as a number of other optimization problems is reduced to packing problem [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Application of Algorithms for Placement of Orthogonal Polyhedrons for Solving the Problems of Packing Objects of Complex Geometric Shape

Chekanin¹,

Chekanin²

2021

EPJ Web Conf.

View full text Add to dashboard Cite

The article is devoted to the development and research of algorithms for placing objects of complex geometric shapes. To solve the placement problem is proposed an approach which consists in transforming the shape of all objects and further application of the developed algorithm for placing orthogonal polyhedrons of arbitrary dimension to the resulting transformed objects. In the process of transforming the shape of the objects being placed, they are initially voxelized, after which the developed decomposition algorithm is applied to the resulting voxelized objects, which provides the formation of orthogonal polyhedrons consisting of the largest possible orthogonal objects. The proposed model of potential containers is used to describe the free space of containers as a set of orthogonal areas. The developed algorithm for the placement of orthogonal polyhedrons provides a fast solution to NP-hard problems of placing objects of complex geometric shapes without resorting to the use of time-consuming nonlinear programming methods. Examples of the practical application of the developed algorithms for modeling the dense layout of parts of complex geometric shapes on the platform of a 3D printer are given.

show abstract

“…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]. All the packing problems including the classic orthogonal packing problem are NP-hard [6,7] and require the use of heuristic [8,9] or metaheuristic optimization algorithms [10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Solving the Problem of Packing Objects of Complex Geometric Shape into a Container of Arbitrary Dimension

Chekanin

2020

Proceedings of the 30th International Conference on Computer Graphics and Machine Vision (GraphiCon 2020). Part 2

View full text Add to dashboard Cite

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.

show abstract

Efficient algorithms for orthogonal packing problems

Cited by 14 publications

References 8 publications

Algorithms for Working with Orthogonal Polyhedrons in Solving Cutting and Packing Problems

Algorithms for Working with Orthogonal Polyhedrons in Solving Cutting and Packing Problems

Application of Algorithms for Placement of Orthogonal Polyhedrons for Solving the Problems of Packing Objects of Complex Geometric Shape

Solving the Problem of Packing Objects of Complex Geometric Shape into a Container of Arbitrary Dimension

Contact Info

Product

Resources

About