A digital distance on the kisrhombille tiling.

IF 1.9 4区材料科学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Acta Crystallographica Section A: Foundations and Advances Pub Date : 2024-05-01 Epub Date: 2024-03-11 DOI:10.1107/S2053273323010628

Fatma Kablan, Béla Vizvári, Benedek Nagy

引用次数: 0

Abstract

The kisrhombille tiling is the dual tessellation of one of the semi-regular tessellations. It consists of right-angled triangle tiles with 12 different orientations. An adequate coordinate system for the tiles of the grid has been defined that allows a formal description of the grid. In this paper, two tiles are considered to be neighbors if they share at least one point in their boundary. Paths are sequences of tiles such that any two consecutive tiles are neighbors. The digital distance is defined as the minimum number of steps in a path between the tiles, and the distance formula is proven through constructing minimum paths. In fact, the distance between triangles is almost twice the hexagonal distance of their embedding hexagons.

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Kisrhombille 瓦上的数字距离。

Kisrhombille 瓦片是半规则瓦片的对偶瓦片。它由 12 个不同方向的直角三角形方格组成。我们已经为网格的瓦片定义了一个适当的坐标系，可以对网格进行正式描述。在本文中，如果两个方格的边界至少有一点是相邻的，那么这两个方格就被认为是相邻的。路径是瓦片的序列，其中任何两个连续的瓦片都是邻居。数字距离被定义为瓦片之间路径的最小步数，距离公式通过构建最小路径来证明。事实上，三角形之间的距离几乎是其嵌入六边形的六边形距离的两倍。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Acta Crystallographica Section A: Foundations and Advances CHEMISTRY, MULTIDISCIPLINARYCRYSTALLOGRAPH-CRYSTALLOGRAPHY

CiteScore

2.60

自引率

11.10%

发文量

419

期刊介绍： Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials. The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial. The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.