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DOI: 10.4230/LIPIcs.SoCG.2022.9

Tighter Bounds for Reconstruction from ε-Samples

Authors: Håvard Bakke Bjerkevik

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

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.

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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)

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@InProceedings{bakkebjerkevik:LIPIcs.SoCG.2022.9,
  author =	{Bakke Bjerkevik, H\r{a}vard},
  title =	{{Tighter Bounds for Reconstruction from \epsilon-Samples}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.9},
  URN =		{urn:nbn:de:0030-drops-160170},
  doi =		{10.4230/LIPIcs.SoCG.2022.9},
  annote =	{Keywords: Curve reconstruction, surface reconstruction, \epsilon-sampling}
}

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Tighter Bounds for Reconstruction from ε-Samples

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