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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. In addition the paper includes a description of how the procedure is modified in order to realise the inner-fit polygon.
CORMSIS-05-05
University of Southampton
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 (2005) A comprehensive and robust procedure for obtaining the nofit polygon using Minkowski sums (Discussion Papers in Centre for Operational Research, Management Science and Information Systems, CORMSIS-05-05) Southampton, GB. University of Southampton

Record type: Monograph (Discussion Paper)

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. In addition the paper includes a description of how the procedure is modified in order to realise the inner-fit polygon.

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Published date: 2005
Organisations: Management

Identifiers

Local EPrints ID: 36850
URI: http://eprints.soton.ac.uk/id/eprint/36850
PURE UUID: 25c84211-668c-4ed9-9be9-e38327dbb62b

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Date deposited: 23 May 2006
Last modified: 17 Jul 2017 15:43

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Contributors

Author: Julia A. Bennell
Author: Xiang Song

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