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On the Topology and Isotopic Meshing of Plane Algebraic Curves
Jin, Kai1; Cheng, Jinsan2
2020-02-01
Source PublicationJOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN1009-6124
Volume33Issue:1Pages:230-260
AbstractThis 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.
KeywordInterval polynomial isotopic meshing plane curve topology
DOI10.1007/s11424-020-8262-5
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Interdisciplinary Applications
WOS IDWOS:000520177000015
PublisherSPRINGER HEIDELBERG
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/51041
Collection中国科学院数学与系统科学研究院
Corresponding AuthorJin, Kai
Affiliation1.Hubei Univ Sci & Technol, Sch Math & Stat, Xianning 437100, Peoples R China
2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Inst Syst Sci, Beijing 100190, Peoples R China
Recommended Citation
GB/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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