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Discrete Linear Geometry on Grid System

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Abstract

We define the algebraic discrete geometry to a 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

    Linh Kieu Troung

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

    Atsushi Imiya

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  1. Linh Kieu Troung
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Correspondence to Atsushi Imiya.

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This article is part of the topical collection “From Geometry to Vision: The Methods for Solving Visual Problems” guest edited by Wei Qi Yan, Harvey Ho, Minh Nguyen and Zhixun Su.

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Troung, L.K., Imiya, A. Discrete Linear Geometry on Grid System. SN COMPUT. SCI. 3, 72 (2022). https://doi.org/10.1007/s42979-021-00937-6

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