A combinatorial technique for generation of digital plane using GCD

IF 1.2 4区计算机科学 Q4 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Annals of Mathematics and Artificial Intelligence Pub Date : 2023-08-28 DOI:10.1007/s10472-023-09889-4

Somrita Saha, Arindam Biswas

引用次数: 0

Abstract

A digital plane is a digitization of a Euclidean plane. A plane is specified by its normal, which is a 3D vector with integer coordinates, as considered in this case. It is established here that a 3D digital straight line segment, shifted by an integer amount, can produce the digitized plane. 3D plane’s normals are classified based on the Greatest Common Divisor (GCD) of its components, and the net code is calculated separately for each case. Experimental results are provided for several normals. Also, we show that the digital plane segment generated is a connected digital plane. The proposed method mainly involves integer arithmetic.

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用GCD生成数字平面的组合技术

数字平面是欧几里得平面的数字化。平面由其法线指定，法线是一个具有整数坐标的三维矢量，如本案例所示。这里可以确定的是，三维数字直线段经过整数偏移后，就能生成数字化平面。三维平面的法线根据其分量的最大公约数（GCD）进行分类，并分别计算每种情况的净码。我们提供了几种法线的实验结果。同时，我们还证明了生成的数字平面段是一个连通的数字平面。建议的方法主要涉及整数运算。

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

Annals of Mathematics and Artificial Intelligence 工程技术-计算机：人工智能

CiteScore

3.00

自引率

8.30%

发文量

审稿时长

>12 weeks

期刊介绍： Annals of Mathematics and Artificial Intelligence presents a range of topics of concern to scholars applying quantitative, combinatorial, logical, algebraic and algorithmic methods to diverse areas of Artificial Intelligence, from decision support, automated deduction, and reasoning, to knowledge-based systems, machine learning, computer vision, robotics and planning. The journal features collections of papers appearing either in volumes (400 pages) or in separate issues (100-300 pages), which focus on one topic and have one or more guest editors. Annals of Mathematics and Artificial Intelligence hopes to influence the spawning of new areas of applied mathematics and strengthen the scientific underpinnings of Artificial Intelligence.