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Discrete Linear Geometry on Non-square Grid

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Geometry and Vision (ISGV 2021)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1386))

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Abstract

We define the algebraic discrete geometry to hexagonal grid system on a plane. Since a hexagon is an element for tiling on a plane, hexagons are suitable as elements of discrete objects. For the description of linear objects in a discrete space, algebraic discrete geometry provides a unified treatment employing double Diophantus equations. Furthermore, we develop an algorithm for the polygonalisation of discrete objects on the hexagonal grid system.

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Authors and Affiliations

  1. School of Science and Technology, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba, 263-8522, Japan

    Troung Kieu Linh

  2. Institute of Management and Information Technologies, Chiba University, Yayoi-cho 1-33, Inage-ku, Chiba, 263-8522, Japan

    Atsushi Imiya

Authors
  1. Troung Kieu Linh
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  2. Atsushi Imiya
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Correspondence to Atsushi Imiya .

Editor information

Editors and Affiliations

  1. Auckland University of Technology, Auckland, New Zealand

    Minh Nguyen

  2. Auckland University of Technology, Auckland, New Zealand

    Wei Qi Yan

  3. Auckland Bioengineering House, Auckland, New Zealand

    Harvey Ho

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Linh, T.K., Imiya, A. (2021). Discrete Linear Geometry on Non-square Grid. In: Nguyen, M., Yan, W.Q., Ho, H. (eds) Geometry and Vision. ISGV 2021. Communications in Computer and Information Science, vol 1386. Springer, Cham. https://doi.org/10.1007/978-3-030-72073-5_17

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  • DOI: https://doi.org/10.1007/978-3-030-72073-5_17

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-72072-8

  • Online ISBN: 978-3-030-72073-5

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