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DOI: 10.4230/LIPIcs.ESA.2019.32

Consistent Digital Curved Rays and Pseudoline Arrangements

Authors: Jinhee Chun, Kenya Kikuchi, and Takeshi Tokuyama

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract

Representing a family of geometric objects in the digital world where each object is represented by a set of pixels is a basic problem in graphics and computational geometry. One important criterion is the consistency, where the intersection pattern of the objects should be consistent with axioms of the Euclidean geometry, e.g., the intersection of two lines should be a single connected component. Previously, the set of linear rays and segments has been considered. In this paper, we extended this theory to families of curved rays going through the origin. We further consider some psudoline arrangements obtained as unions of such families of rays.

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Jinhee Chun, Kenya Kikuchi, and Takeshi Tokuyama. Consistent Digital Curved Rays and Pseudoline Arrangements. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 32:1-32:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chun_et_al:LIPIcs.ESA.2019.32,
  author =	{Chun, Jinhee and Kikuchi, Kenya and Tokuyama, Takeshi},
  title =	{{Consistent Digital Curved Rays and Pseudoline Arrangements}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.32},
  URN =		{urn:nbn:de:0030-drops-111538},
  doi =		{10.4230/LIPIcs.ESA.2019.32},
  annote =	{Keywords: Computational Geometry, Digital Geometry, Spanning Tree, Graph Drawing}
}

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Consistent Digital Curved Rays and Pseudoline Arrangements

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