Abstract
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.
Highlights
The problem of packing objects of complex geometric shape has a large number of practical applications in various areas
Modern methods for solving problems of packing objects of complex geometric shape are based on the use of the hodograph vector function of dense placement, which requires the subsequent application of nonlinear programming methods characterized by high computational complexity [7,8,9,10,11,12]
To reduce the complexity of the problem, we propose an approach that consists in packing of voxelized objects [13,14,15] by applying the developed algorithm of placement of orthogonal polyhedrons
Summary
The problem of packing objects of complex geometric shape has a large number of practical applications in various areas. Modern methods for solving problems of packing objects of complex geometric shape are based on the use of the hodograph vector function of dense placement, which requires the subsequent application of nonlinear programming methods characterized by high computational complexity [7,8,9,10,11,12]. To reduce the complexity of the problem, we propose an approach that consists in packing of voxelized objects [13,14,15] by applying the developed algorithm of placement of orthogonal polyhedrons. In the particular case, when all orthogonal polyhedrons consist of only one orthogonal object mi = 1 ∀i ∈{1, , n}, the considered problem will be reduced to the classic D -dimensional orthogonal packing problem [1, 2]
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