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Computing Non-Obtuse Triangulations with Few Steiner Points (CG Challenge)

Authors Mikkel Abrahamsen , Florestan Brunck , Jacobus Conradi , Benedikt Kolbe , André Nusser

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ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • non-obtuse triangulation
  • local search
  • competition

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Abstract

We present the winning implementation of the Seventh Computational Geometry Challenge (CG:SHOP 2025). The task in this challenge was to find non-obtuse triangulations for given planar regions, respecting a given set of constraints consisting of extra vertices and edges that must be part of the triangulation. The goal was to minimize the number of introduced Steiner points. Our approach is to maintain a constrained Delaunay triangulation, for which we repeatedly remove, relocate, or add Steiner points. We use local search to choose the action that improves the triangulation the most, until the resulting triangulation is non-obtuse.

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Mikkel Abrahamsen, Florestan Brunck, Jacobus Conradi, Benedikt Kolbe, and André Nusser. Computing Non-Obtuse Triangulations with Few Steiner Points (CG Challenge). In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 79:1-79:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SoCG.2025.79

Author Details

Mikkel Abrahamsen
  • University of Copenhagen, Denmark
Florestan Brunck
  • University of Copenhagen, Denmark
Jacobus Conradi
  • University of Bonn, Germany
Benedikt Kolbe
  • Hausdorff Center for Mathematics, Lamarr Institute for Machine Learning and Artificial Intelligence, University of Bonn, Germany
André Nusser
  • Université Côte d'Azur, CNRS, Inria, Sophia Antipolis, France

Funding

  • Abrahamsen, Mikkel: Supported by Independent Research Fund Denmark, grant 1054-00032B, and by the Carlsberg Foundation, grant CF24-1929.
  • Brunck, Florestan: Supported by a DNRF Chair grant from the Danish National Research Foundation and partially by the BARC grant of the Villum Foundation.
  • Conradi, Jacobus: Funded by the iBehave Network: Sponsored by the Ministry of Culture and Science of the State of North Rhine-Westphalia.
  • Kolbe, Benedikt: This research has partly been funded by the Federal Ministry of Education and Research of Germany and the state of North-Rhine Westphalia as part of the Lamarr-Institute for Machine Learning and Artificial Intelligence.
  • Nusser, André: Supported by the France 2030 investment plan managed by the ANR as part of the Initiative of Excellence of Université Côte d'Azur with reference number ANR-15-IDEX-01.

Acknowledgements

We thank the Challenge organizers and other competitors for their time, feedback, and making this whole event possible. We thank Max Kanold for invaluable input enabling high quality visualizations which made later discussions on how to improve our algorithm all the more fruitful. We gratefully acknowledge the access to the Marvin cluster of the University of Bonn.

Supplementary Materials

References

  1. Mikkel Abrahamsen, Florestan Brunck, Jacobus Conradi, Benedikt Kolbe, and André Nusser. nonObtuseTri. Software, version v3.0., (visited on 2025-06-02). URL: https://github.com/JacobusTheSecond/nonObtuseTri
    Software Heritage Logo archived version
    full metadata available at: https://doi.org/10.4230/artifacts.23288
  2. Taehoon Ahn, Jaegun Lee, Byeonguk Kang, and Hwi Kim. Incremental algorithm and local search for minimum non-obtuse triangulations (CG challenge). In Oswin Aichholzer and Haitao Wang, editors, 41st International Symposium on Computational Geometry (SoCG 2025), 2025. These proceedings. URL: https://doi.org/10.4230/LIPIcs.SoCG.2025.80.
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