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Priority-Driven Nesting of Irregular Polygonal Shapes Within a Convex Polygonal Container Based on a Hierarchical Integer Grid (CG Challenge)

Author Martin Held

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LIPIcs.SoCG.2024.85.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Computational Geometry
  • geometric optimization
  • nesting
  • packing
  • algorithm engineering

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Abstract

Our work on nesting polygons is based on two key components: (1) a hierarchy of uniform integer grids for maintaining free space within the container during the nesting such that placement queries can be answered reasonably efficiently, and (2) priority heuristics for choosing the order in which the polygons are tested for placement. We discuss our approach and shed a light on the results obtained.

Cite As Get BibTex

Martin Held. Priority-Driven Nesting of Irregular Polygonal Shapes Within a Convex Polygonal Container Based on a Hierarchical Integer Grid (CG Challenge). In 40th International Symposium on Computational Geometry (SoCG 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 293, pp. 85:1-85:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.SoCG.2024.85

Author Details

Martin Held
  • FB Informatik, Universität Salzburg, Austria

References

  1. Alkan Atak, Kevin Buchin, Mart Hagedoorn, Jona Heinrichs, Karsten Hogreve, Guangping Li, and Patrick Pawelczyk. Computing maximum polygonal packings in convex polygons using best-fit, genetic algorithms and ILPs. In Symposium on Computational Geometry (SoCG), volume 293 of LIPIcs, pages 83:1-83:9, 2024. URL: https://doi.org/10.4230/LIPIcs.SoCG.2024.83.
  2. Guilherme Dias da Fonseca and Yan Gerard. Shadoks approach to knapsack polygonal packing. In Symposium on Computational Geometry (SoCG), volume 293 of LIPIcs, pages 84:1-84:9, 2024. URL: https://doi.org/10.4230/LIPIcs.SoCG.2024.84.
  3. Canhui Luo, Zhouxing Su, and Zhipeng Lü. A general heuristic approach for maximum polygon packing. In Symposium on Computational Geometry (SoCG), volume 293 of LIPIcs, pages 86:1-86:9, 2024. URL: https://doi.org/10.4230/LIPIcs.SoCG.2024.86.
  4. Sándor P. Fekete, Phillip Keldenich, Dominik Krupke, and Stefan Schirra. Maximum polygon packing: The CG:SHOP Challenge 2024, 2024. URL: https://arxiv.org/abs/2403.16203.
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