On the Topology and Isotopic Meshing of Plane Algebraic Curves

doi:10.1007/s11424-020-8262-5

	On the Topology and Isotopic Meshing of Plane Algebraic Curves
	Jin, Kai 1; Cheng, Jinsan 2
刊名	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
	2020-02-01
卷号	33 期号:1 页码:230-260
关键词	Interval polynomial isotopic meshing plane curve topology
ISSN号	1009-6124
DOI	10.1007/s11424-020-8262-5
英文摘要	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.
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000520177000015
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/51040]
专题	中国科学院数学与系统科学研究院
通讯作者	Jin, Kai
作者单位	1.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
推荐引用方式 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.