{"title":"用GCD生成数字平面的组合技术","authors":"Somrita Saha, Arindam Biswas","doi":"10.1007/s10472-023-09889-4","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":7971,"journal":{"name":"Annals of Mathematics and Artificial Intelligence","volume":"92 1","pages":"139 - 167"},"PeriodicalIF":1.2000,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A combinatorial technique for generation of digital plane using GCD\",\"authors\":\"Somrita Saha, Arindam Biswas\",\"doi\":\"10.1007/s10472-023-09889-4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>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.</p></div>\",\"PeriodicalId\":7971,\"journal\":{\"name\":\"Annals of Mathematics and Artificial Intelligence\",\"volume\":\"92 1\",\"pages\":\"139 - 167\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2023-08-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annals of Mathematics and Artificial Intelligence\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10472-023-09889-4\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of Mathematics and Artificial Intelligence","FirstCategoryId":"94","ListUrlMain":"https://link.springer.com/article/10.1007/s10472-023-09889-4","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE","Score":null,"Total":0}
A combinatorial technique for generation of digital plane using GCD
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.
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.
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