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Tighter Bounds for Reconstruction from ε-Samples

Author Håvard Bakke Bjerkevik

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

Funding

The author is supported by the Austrian Science Fund (FWF) grant number P 33765-N.

Acknowledgements

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.

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.SoCG.2022.9

Abstract

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
Keywords
  • Curve reconstruction
  • surface reconstruction
  • ε-sampling

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