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Consistent Digital Curved Rays and Pseudoline Arrangements

Authors Jinhee Chun, Kenya Kikuchi, Takeshi Tokuyama

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Author Details

Jinhee Chun
  • GSIS Tohoku University, Sendai, Miyagi, Japan
Kenya Kikuchi
  • GSIS Tohoku University, Sendai, Miyagi, Japan
Takeshi Tokuyama
  • Kwansei-Gakuin University, Sanda, Hyōgo, Japan

Funding

This work is partially supported by MEXT JSPS Kakenhi 17K19954, 17K00002 and 18H05291.

Cite AsGet BibTex

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)
https://doi.org/10.4230/LIPIcs.ESA.2019.32

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computational geometry
Keywords
  • Computational Geometry
  • Digital Geometry
  • Spanning Tree
  • Graph Drawing

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