Isotopic Meshing of a Real Algebraic Space Curve

doi:10.1007/s11424-020-8378-7

CSpace > 系统科学研究所

	Isotopic Meshing of a Real Algebraic Space Curve
	Jin, Kai 1; Cheng, Jinsan2
	2020-08-01
发表期刊	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN	1009-6124
卷号	33 期号:4 页码:1275-1296
摘要	This paper presents a new algorithm for computing the topology of an algebraic space curve. Based on an efficient weak generic position-checking method and a method for solving bivariate polynomial systems, the authors give a first deterministic and efficient algorithm to compute the topology of an algebraic space curve. Compared to extant methods, the new algorithm is efficient for two reasons. The bit size of the coefficients appearing in the sheared polynomials are greatly improved. The other is that one projection is enough for most general cases in the new algorithm. After the topology of an algebraic space curve is given, the authors also provide an isotopic-meshing (approximation) of the space curve. Moreover, an approximation of the algebraic space curve can be generated automatically if the approximations of two projected plane curves are first computed. This is also an advantage of our method. Many non-trivial experiments show the efficiency of the algorithm.
关键词	Algebraic space curve topology weak generic position
DOI	10.1007/s11424-020-8378-7
收录类别	SCI
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000557013600022
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51959
专题	系统科学研究所
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. Isotopic Meshing of a Real Algebraic Space Curve[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2020,33(4):1275-1296.
APA	Jin, Kai,&Cheng, Jinsan.(2020).Isotopic Meshing of a Real Algebraic Space Curve.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,33(4),1275-1296.
MLA	Jin, Kai,et al."Isotopic Meshing of a Real Algebraic Space Curve".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY 33.4(2020):1275-1296.