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 On the Topology and Isotopic Meshing of Plane Algebraic Curves Jin, Kai1; Cheng, Jinsan2 2020-02-01 Source Publication JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY ISSN 1009-6124 Volume 33Issue:1Pages:230-260 Abstract This paper presents a symbolic algorithm to compute the topology of a plane curve. This is a full version of the authors' CASC15 paper. The algorithm mainly involves resultant computations and real root isolation for univariate polynomials. Compared to other symbolic methods based on elimination techniques, the novelty of the proposed method is that the authors use a technique of interval polynomials to solve the system {f(alpha,y), partial differential f partial differential y(alpha,y)}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left\{ {f(\alpha ,y),\tfrac{{\partial f}}{{\partial y}}(\alpha ,y)} \right\}$$\end{document} and simultaneously obtain numerous simple roots of f(alpha, y) = 0 on the alpha fiber. This significantly improves the efficiency of the lifting step because the authors are no longer required to compute the simple roots of f(alpha, y) = 0. After the topology is computed, a revised Newton's method is presented to compute an isotopic meshing of the plane algebraic curve. Though the approximation method is numerical, the authors can ensure that the proposed method is a certified one, and the meshing is topologically correct. Several nontrivial examples confirm that the proposed algorithm performs well. Keyword Interval polynomial isotopic meshing plane curve topology DOI 10.1007/s11424-020-8262-5 Indexed By SCI Language 英语 WOS Research Area Mathematics WOS Subject Mathematics, Interdisciplinary Applications WOS ID WOS:000520177000015 Publisher SPRINGER HEIDELBERG Citation statistics Document Type 期刊论文 Identifier http://ir.amss.ac.cn/handle/2S8OKBNM/51041 Collection 中国科学院数学与系统科学研究院 Corresponding Author Jin, Kai Affiliation 1.Hubei Univ Sci & Technol, Sch Math & Stat, Xianning 437100, Peoples R China2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Inst Syst Sci, Beijing 100190, Peoples R China Recommended CitationGB/T 7714 Jin, Kai,Cheng, Jinsan. On the Topology and Isotopic Meshing of Plane Algebraic Curves[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2020,33(1):230-260. APA Jin, Kai,&Cheng, Jinsan.(2020).On the Topology and Isotopic Meshing of Plane Algebraic Curves.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,33(1),230-260. MLA Jin, Kai,et al."On the Topology and Isotopic Meshing of Plane Algebraic Curves".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 33.1(2020):230-260.
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