Frontiers in Computational Geometry

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (28 February 2022) | Viewed by 2971

Special Issue Editors


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Guest Editor
Division of AI Computer Science and Engineering, Kyonggi University, Suwon 16227, Korea
Interests: computational geometry; discrete geometry; algorithms design and Analysis; theoretical computer science

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Guest Editor
Division of Computer and Electronic Systems, Hankuk University of Foreign Studies 107, Imun-ro, Dongdaemun-gu, Seoul 130-791, Korea
Interests: computational geometry; graph drawing; algorithms and data structures

Special Issue Information

Dear Colleagues,

Computational geometry is a discipline of computer science devoted to the study of problems which can be stated in terms of geometric objects, such as points, lines, circles, and other structures in geometric spaces. It has successfully been developed and grown since the 1970s with the beauty and symmetry unveiled from geometry and its remarkable scientific achievements: efficient algorithms for practical problems, combinatorial discoveries on important geometric structures, and their applications to a broad range of science and engineering fields, including computer graphics, computer vision, computer-aided design and manufacturing, pattern recognition, wireless networks, spatial databases and geographic information systems, and bioinformatics.

The aim of the present Special Issue is to promote research that lies at the frontier of computational geometry, both in theory and applications. We are soliciting research and review articles covering a wide range of topics on computational geometry, including (though not limited to) the following:

  • Design, analysis, and implementation of geometric algorithms and data structures;
  • Computational complexity of geometric problems;
  • Discrete and combinatorial geometry;
  • Computational topology;
  • Applications of computational geometry in any field.

Please note that all submitted papers must be within the general scope of the Symmetry journal.

Dr. Sang Won Bae
Prof. Dr. Chan-Su Shin
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Geometric algorithms and data structures
  • Computational complexity of geometric problems
  • Discrete and combinatorial geometry
  • Computational topology
  • Applications of computational geometry

Published Papers (1 paper)

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Research

23 pages, 28600 KiB  
Article
Partial Covering of a Circle by 6 and 7 Congruent Circles
by Zsolt Gáspár, Tibor Tarnai and Krisztián Hincz
Symmetry 2021, 13(11), 2133; https://doi.org/10.3390/sym13112133 - 09 Nov 2021
Viewed by 2087
Abstract
Background: Some medical and technological tasks lead to the geometrical problem of how to cover the unit circle as much as possible by n congruent circles of given radius r, while r varies from the radius in the maximum packing to the [...] Read more.
Background: Some medical and technological tasks lead to the geometrical problem of how to cover the unit circle as much as possible by n congruent circles of given radius r, while r varies from the radius in the maximum packing to the radius in the minimum covering. Proven or conjectural solutions to this partial covering problem are known only for n = 2 to 5. In the present paper, numerical solutions are given to this problem for n = 6 and 7. Method: The method used transforms the geometrical problem to a mechanical one, where the solution to the geometrical problem is obtained by finding the self-stress positions of a generalised tensegrity structure. This method was developed by the authors and was published in an earlier publication. Results: The method applied results in locally optimal circle arrangements. The numerical data for the special circle arrangements are presented in a tabular form, and in drawings of the arrangements. Conclusion: It was found that the case of n = 6 is very complicated, whilst the case n = 7 is very simple. It is shown in this paper that locally optimal arrangements may exhibit different types of symmetry, and equilibrium paths may bifurcate. Full article
(This article belongs to the Special Issue Frontiers in Computational Geometry)
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