出租车距离均值函数及其几何应用:方法、实现和实例

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, SOFTWARE ENGINEERING

Fundamenta Informaticae Pub Date : 2023-08-01 DOI:10.3233/fi-222156

Csaba Vincze, Ábris Nagy

{"title":"出租车距离均值函数及其几何应用:方法、实现和实例","authors":"Csaba Vincze, Ábris Nagy","doi":"10.3233/fi-222156","DOIUrl":null,"url":null,"abstract":"A distance mean function measures the average distance of points from the elements of a given set of points (focal set) in the space. The level sets of a distance mean function are called generalized conics. In case of infinite focal points the average distance is typically given by integration over the focal set. The paper contains a survey on the applications of taxicab distance mean functions and generalized conics’ theory in geometric tomography: bisection of the focal set and reconstruction problems by coordinate X-rays. The theoretical results are illustrated by implementations in Maple, methods and examples as well.1","PeriodicalId":56310,"journal":{"name":"Fundamenta Informaticae","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Taxicab Distance Mean Functions and their Geometric Applications: Methods, Implementations and Examples\",\"authors\":\"Csaba Vincze, Ábris Nagy\",\"doi\":\"10.3233/fi-222156\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A distance mean function measures the average distance of points from the elements of a given set of points (focal set) in the space. The level sets of a distance mean function are called generalized conics. In case of infinite focal points the average distance is typically given by integration over the focal set. The paper contains a survey on the applications of taxicab distance mean functions and generalized conics’ theory in geometric tomography: bisection of the focal set and reconstruction problems by coordinate X-rays. The theoretical results are illustrated by implementations in Maple, methods and examples as well.1\",\"PeriodicalId\":56310,\"journal\":{\"name\":\"Fundamenta Informaticae\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2023-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fundamenta Informaticae\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3233/fi-222156\",\"RegionNum\":4,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"COMPUTER SCIENCE, SOFTWARE ENGINEERING\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamenta Informaticae","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3233/fi-222156","RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, SOFTWARE ENGINEERING","Score":null,"Total":0}

引用次数: 0

摘要

距离平均函数测量点到空间中给定点集(焦点集)元素的平均距离。距离均值函数的水平集称为广义二次曲线。在无限焦点的情况下，平均距离通常由对焦点集的积分给出。本文综述了出租车距离平均函数和广义二次曲线理论在几何层析成像、焦点集平分和坐标x射线重建问题中的应用。通过在Maple中的实现、方法和实例对理论结果进行了说明

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On Taxicab Distance Mean Functions and their Geometric Applications: Methods, Implementations and Examples

A distance mean function measures the average distance of points from the elements of a given set of points (focal set) in the space. The level sets of a distance mean function are called generalized conics. In case of infinite focal points the average distance is typically given by integration over the focal set. The paper contains a survey on the applications of taxicab distance mean functions and generalized conics’ theory in geometric tomography: bisection of the focal set and reconstruction problems by coordinate X-rays. The theoretical results are illustrated by implementations in Maple, methods and examples as well.1

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Fundamenta Informaticae 工程技术-计算机：软件工程

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

9.8 months

期刊介绍： Fundamenta Informaticae is an international journal publishing original research results in all areas of theoretical computer science. Papers are encouraged contributing: solutions by mathematical methods of problems emerging in computer science solutions of mathematical problems inspired by computer science. Topics of interest include (but are not restricted to): theory of computing, complexity theory, algorithms and data structures, computational aspects of combinatorics and graph theory, programming language theory, theoretical aspects of programming languages, computer-aided verification, computer science logic, database theory, logic programming, automated deduction, formal languages and automata theory, concurrency and distributed computing, cryptography and security, theoretical issues in artificial intelligence, machine learning, pattern recognition, algorithmic game theory, bioinformatics and computational biology, quantum computing, probabilistic methods, algebraic and categorical methods.