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A comprehensive and robust procedure for obtaining the nofit polygon using Minkowski sums

A comprehensive and robust procedure for obtaining the nofit polygon using Minkowski sums
A comprehensive and robust procedure for obtaining the nofit polygon using Minkowski sums
The nofit polygon is a powerful and effective tool for handling the geometric requirements of solution approaches to irregular cutting and packing problems. Although the concept was first described in 1966, it was not until the early 90s that the general trend of research moved away from direct trigonometry to favour the nofit polygon. Since then, the ability to calculate the nofit polygon has practically become a pre-requisite for researching irregular packing problems. However, realisation of this concept in the form of a robust algorithm is a highly challenging task with few instructive approaches published. In this paper, a procedure using the mathematical concept of Minkowski sums for the calculation of the nofit polygon is presented. The described procedure is more robust than other approaches using Minkowski Sum knowledge and includes details of the removal of internal edges to find holes, slits and lock and key positions. The procedure is tested on benchmark data sets and gives examples of complicated cases.
cutting and packing, nesting, geometric algorithms, configuration space
0305-0548
267-281
Bennell, Julia A.
38d924bc-c870-4641-9448-1ac8dd663a30
Song, Xiang
28fc03d0-9077-49f5-bc94-a4f92fa76565
Bennell, Julia A.
38d924bc-c870-4641-9448-1ac8dd663a30
Song, Xiang
28fc03d0-9077-49f5-bc94-a4f92fa76565

Bennell, Julia A. and Song, Xiang (2008) A comprehensive and robust procedure for obtaining the nofit polygon using Minkowski sums. [in special issue: Part Special Issue: Applications of OR in Finance] Computers & Operations Research, 35 (1), 267-281. (doi:10.1016/j.cor.2006.02.026).

Record type: Article

Abstract

The nofit polygon is a powerful and effective tool for handling the geometric requirements of solution approaches to irregular cutting and packing problems. Although the concept was first described in 1966, it was not until the early 90s that the general trend of research moved away from direct trigonometry to favour the nofit polygon. Since then, the ability to calculate the nofit polygon has practically become a pre-requisite for researching irregular packing problems. However, realisation of this concept in the form of a robust algorithm is a highly challenging task with few instructive approaches published. In this paper, a procedure using the mathematical concept of Minkowski sums for the calculation of the nofit polygon is presented. The described procedure is more robust than other approaches using Minkowski Sum knowledge and includes details of the removal of internal edges to find holes, slits and lock and key positions. The procedure is tested on benchmark data sets and gives examples of complicated cases.

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More information

Published date: 1 January 2008
Keywords: cutting and packing, nesting, geometric algorithms, configuration space
Organisations: Management

Identifiers

Local EPrints ID: 154799
URI: https://eprints.soton.ac.uk/id/eprint/154799
ISSN: 0305-0548
PURE UUID: 085aa0c4-d182-4e2d-80cc-3d1db6a6e8b9

Catalogue record

Date deposited: 26 May 2010 08:42
Last modified: 16 Jul 2019 23:58

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