License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2022.58
URN: urn:nbn:de:0030-drops-158680
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/15868/
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Tokuyama, Takeshi ; Yoshimura, Ryo

High Quality Consistent Digital Curved Rays via Vector Field Rounding

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LIPIcs-STACS-2022-58.pdf (1 MB)

Abstract

We consider the consistent digital rays (CDR) of curved rays, which approximates a set of curved rays emanating from the origin by the set of rooted paths (called digital rays) of a spanning tree of a grid graph. Previously, a construction algorithm of CDR for diffused families of curved rays to attain an O(√{n log n}) bound for the distance between digital ray and the corresponding ray is known [Chun et al., 2019]. In this paper, we give a description of the problem as a rounding problem of the vector field generated from the ray family, and investigate the relation of the quality of CDR and the discrepancy of the range space generated from gradient curves of rays. Consequently, we show the existence of a CDR with an O(log ^{1.5} n) distance bound for any diffused family of curved rays.

BibTeX - Entry

@InProceedings{tokuyama_et_al:LIPIcs.STACS.2022.58,
  author =	{Tokuyama, Takeshi and Yoshimura, Ryo},
  title =	{{High Quality Consistent Digital Curved Rays via Vector Field Rounding}},
  booktitle =	{39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)},
  pages =	{58:1--58:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-222-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{219},
  editor =	{Berenbrink, Petra and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/15868},
  URN =		{urn:nbn:de:0030-drops-158680},
  doi =		{10.4230/LIPIcs.STACS.2022.58},
  annote =	{Keywords: Computational Geometry, Discrepancy Theory, Consistent Digital Rays, Digital Geometry}
}

Keywords: Computational Geometry, Discrepancy Theory, Consistent Digital Rays, Digital Geometry
Collection: 39th International Symposium on Theoretical Aspects of Computer Science (STACS 2022)
Issue Date: 2022
Date of publication: 09.03.2022

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