Raster-based mathematical morphology for cutting and packing problems

2021 ◽  
Author(s):  
Fernanda Miyuki Yamada ◽  
Hiroki Takahashi ◽  
Harlen Costa Batagelo ◽  
João Paulo Gois
Keyword(s):  
Mathematical Morphology ◽  
Cutting And Packing ◽  
Packing Problems

scholarly journals A survey on the cutting and packing problems

2020 ◽  
Vol 13 (4) ◽  
pp. 567-572
Author(s):  
Loris Faina
Keyword(s):  
Three Dimensional ◽  
Cutting And Packing ◽  
Unified Approach ◽  
Geometrical Method ◽  
Packing Problems ◽  
Enumeration Scheme

Abstract This paper presents a unified approach, based on a geometrical method (see Faina in Eur J Oper Res 114:542–556, 1999; Eur J Oper Res 126:340–354, 2000), which reduces the general two and three dimensional cutting and packing type problems to a finite enumeration scheme.

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

2021 ◽  
Author(s):  
Vladislav Chekanin ◽  
Alexander Chekanin
Keyword(s):  
Complex Shape ◽  
Three Dimensional ◽  
Geometric Transformation ◽  
Cutting And Packing ◽  
Packing Problems ◽  
Basic Model ◽  
Composite Objects ◽  
Hard Problems ◽  
Orthogonal Polyhedron ◽  
Polygonal Model

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.

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