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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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Multimedia Contribution

DOI: 10.4230/LIPIcs.SoCG.2017.64

Folding Free-Space Diagrams: Computing the Fréchet Distance between 1-Dimensional Curves (Multimedia Contribution)

Authors: Kevin Buchin, Jinhee Chun, Maarten Löffler, Aleksandar Markovic, Wouter Meulemans, Yoshio Okamoto, and Taichi Shiitada

Published in: LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)

Abstract

By folding the free-space diagram for efficient preprocessing, we show that the Frechet distance between 1D curves can be computed in O(nk log n) time, assuming one curve has ply k.

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Kevin Buchin, Jinhee Chun, Maarten Löffler, Aleksandar Markovic, Wouter Meulemans, Yoshio Okamoto, and Taichi Shiitada. Folding Free-Space Diagrams: Computing the Fréchet Distance between 1-Dimensional Curves (Multimedia Contribution). In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 64:1-64:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{buchin_et_al:LIPIcs.SoCG.2017.64,
  author =	{Buchin, Kevin and Chun, Jinhee and L\"{o}ffler, Maarten and Markovic, Aleksandar and Meulemans, Wouter and Okamoto, Yoshio and Shiitada, Taichi},
  title =	{{Folding Free-Space Diagrams: Computing the Fr\'{e}chet Distance between 1-Dimensional Curves}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{64:1--64:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Aronov, Boris and Katz, Matthew J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.64},
  URN =		{urn:nbn:de:0030-drops-72417},
  doi =		{10.4230/LIPIcs.SoCG.2017.64},
  annote =	{Keywords: Frechet distance, ply, k-packed curves}
}

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Documents authored by Chun, Jinhee

Consistent Digital Curved Rays and Pseudoline Arrangements

Abstract

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Folding Free-Space Diagrams: Computing the Fréchet Distance between 1-Dimensional Curves (Multimedia Contribution)

Abstract

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