Partitioning Orthogonal Histograms into Rectangular Boxes

Biedl, Thérèse; Derka, Martin; Irvine, Veronika; Lubiw, Anna; Mondal, Debajyoti; Turcotte, Alexi

doi:10.1007/978-3-319-77404-6_12

Cited by 5 publications

(2 citation statements)

References 12 publications

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“…This model allows switch from use the timeconsuming nonlinear programming methods (which are applied for placing objects specified by polygonal modeling, the practical application of which is limited only by the small size of the problem) to methods developed for placing voxelized objects. Unlike decomposition algorithms developed by other authors [28][29][30], the proposed algorithm is described and programmatically implemented invariantly with respect to the dimension of the problem to be solved. The developed algorithm provides decomposition of orthogonal polyhedrons of arbitrary shape, including those with holes or internal cavities.…”

Section: Resultsmentioning

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

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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.

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Section: Resultsmentioning

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

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“…Unlike decomposition algorithms developed by other authors [20][21][22], the proposed algorithm is described and programmatically implemented invariantly with respect to the dimension of the problem to be solved.…”

Section: Fig 4 Addition Operationmentioning

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.

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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.

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Solving the Problem of Decomposition of an Orthogonal Polyhedron of Arbitrary Dimension

Chekanin

2020

Advances in Mechanical Engineering

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Partitioning Orthogonal Histograms into Rectangular Boxes

Cited by 5 publications

References 12 publications

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

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

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

Solving the Problem of Decomposition of an Orthogonal Polyhedron of Arbitrary Dimension

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