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The irregular nesting problem: a new approach for nofit polygon calculation

Author

Listed:
  • L Huyao

    (Shanghai Jiaotong University)

  • H Yuanjun

    (Shanghai Jiaotong University)

  • J A Bennell

    (University of Southampton)

Abstract

This paper presents a new approach for generating the nofit polygon (NFP) that is simple, intuitive and computationally efficient. The NFP has in recent years become an important tool for handling the geometric calculations for two-dimensional irregular shape nesting problems. Its value lies in reducing the computational complexity of detecting whether two polygons overlap. The proposed NFP generator is based on the novel concept of trace line segments that are derived from the interaction of the two-component polygons. The complete set of the trace line segments contain all the boundary edges of the NFP and some internal points that need to be discarded. Algorithms for deriving the trace line segments, efficiently determining those segments that form the boundary of the NFP and the identification of holes and degenerate cases are described.

Suggested Citation

  • L Huyao & H Yuanjun & J A Bennell, 2007. "The irregular nesting problem: a new approach for nofit polygon calculation," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(9), pages 1235-1245, September.
    • Handle: RePEc:pal:jorsoc:v:58:y:2007:i:9:d:10.1057_palgrave.jors.2602255
    DOI: 10.1057/palgrave.jors.2602255
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    References listed on IDEAS

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    1. P D Watson & A M Tobias, 1999. "An efficient algorithm for the regular W1 packing of polygons in the infinite plane," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(10), pages 1054-1062, October.
    2. Li, Zhenyu & Milenkovic, Victor, 1995. "Compaction and separation algorithms for non-convex polygons and their applications," European Journal of Operational Research, Elsevier, vol. 84(3), pages 539-561, August.
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    Cited by:

    1. Qiang Luo & Yunqing Rao, 2022. "Improved Sliding Algorithm for Generating No-Fit Polygon in the 2D Irregular Packing Problem," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    2. E. K. Burke & R. S. R. Hellier & G. Kendall & G. Whitwell, 2010. "Irregular Packing Using the Line and Arc No-Fit Polygon," Operations Research, INFORMS, vol. 58(4-part-1), pages 948-970, August.

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