Tighter Bounds for Reconstruction from ε-Samples

Author Håvard Bakke Bjerkevik

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Author Details

Håvard Bakke Bjerkevik
  • Institute of Geometry, Technische Universität Graz, Austria


The author would like to thank Michael Kerber for insights into the size of Delaunay triangulations, and Stefan Ohrhallinger and Scott A. Mitchell for answering my questions about the state of the art of curve and surface reconstruction.

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Håvard Bakke Bjerkevik. Tighter Bounds for Reconstruction from ε-Samples. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


We show that reconstructing a curve in ℝ^d for d ≥ 2 from a 0.66-sample is always possible using an algorithm similar to the classical NN-Crust algorithm. Previously, this was only known to be possible for 0.47-samples in ℝ² and 1/3-samples in ℝ^d for d ≥ 3. In addition, we show that there is not always a unique way to reconstruct a curve from a 0.72-sample; this was previously only known for 1-samples. We also extend this non-uniqueness result to hypersurfaces in all higher dimensions.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Geometric topology
  • Curve reconstruction
  • surface reconstruction
  • ε-sampling


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