Tighter Bounds for Reconstruction from ε-Samples

Havard Bakke Bjerkevik

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review

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 R 2 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.

Original languageEnglish
Title of host publication38th International Symposium on Computational Geometry (SoCG 2022)
EditorsXavier Goaoc, Michael Kerber
PublisherSchloss Dagstuhl - Leibniz-Zentrum für Informatik
Pages9:1-9:17
ISBN (Electronic) 978-3-95977-227-3
DOIs
Publication statusPublished - 1 Jun 2022
Event38th International Symposium on Computational Geometry: SoCG 2022 - Berlin, Germany, Berlin, Germany
Duration: 7 Jun 202210 Jun 2022
https://www.inf.fu-berlin.de/inst/ag-ti/socg22/socg.html

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume224
ISSN (Print)1868-8969

Conference

Conference38th International Symposium on Computational Geometry
Abbreviated titleSoCG 2022
Country/TerritoryGermany
CityBerlin
Period7/06/2210/06/22
Internet address

Keywords

  • ?-sampling
  • Curve reconstruction
  • surface reconstruction

ASJC Scopus subject areas

  • Software

Fields of Expertise

  • Information, Communication & Computing

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