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 language | English |
|---|---|
| Title of host publication | 38th International Symposium on Computational Geometry (SoCG 2022) |
| Editors | Xavier Goaoc, Michael Kerber |
| Publisher | Schloss Dagstuhl - Leibniz-Zentrum für Informatik |
| Pages | 9:1-9:17 |
| ISBN (Electronic) | 978-3-95977-227-3 |
| DOIs | |
| Publication status | Published - 1 Jun 2022 |
| Event | 38th International Symposium on Computational Geometry: SoCG 2022 - Berlin, Germany, Berlin, Germany Duration: 7 Jun 2022 → 10 Jun 2022 https://www.inf.fu-berlin.de/inst/ag-ti/socg22/socg.html |
Publication series
| Name | Leibniz International Proceedings in Informatics, LIPIcs |
|---|---|
| Volume | 224 |
| ISSN (Print) | 1868-8969 |
Conference
| Conference | 38th International Symposium on Computational Geometry |
|---|---|
| Abbreviated title | SoCG 2022 |
| Country/Territory | Germany |
| City | Berlin |
| Period | 7/06/22 → 10/06/22 |
| Internet address |
Keywords
- ?-sampling
- Curve reconstruction
- surface reconstruction
ASJC Scopus subject areas
- Software
Fields of Expertise
- Information, Communication & Computing