Survey on the theory and applications of mu-bases for rational curves and surfaces

doi:10.1016/j.cam.2017.07.023

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	Survey on the theory and applications of mu-bases for rational curves and surfaces
	Jia, Xiaohong1 ; Shi, Xiaoran 2; Chen, Falai 3
	2018-02-01
发表期刊	JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN	0377-0427
卷号	329 页码:2-23
摘要	mu-Bases are new representations for rational curves and surfaces which serve as a bridge between their parametric forms and implicit forms. Geometrically, mu-bases are represented by moving lines or moving planes, while their algebraic counterparts are special syzygies of the parametric equations of rational curves or surfaces. mu-bases have been proven to be significant in solving many important problems in geometric modeling, such as fast implicitization, singularity computation, reparametrization as well as providing easy inversion formulas for points. We review the state-of-the-art results in mu-bases theory and applications for rational curves and surfaces, and raise unsolved problems for future research. (C) 2017 Elsevier B.V. All rights reserved.
关键词	Rational curve/surface mu-basis Syzygy Parametrization Implicitization Singularity computation
DOI	10.1016/j.cam.2017.07.023
语种	英语
资助项目	NSFC[11571338] ; NSFC[11301116] ; National Laboratory of Pattern Recognition (NLPR)[201700020] ; Postdoctoral Science Foundation[2016T90272] ; Postdoctoral Science Foundation[LBH-Z14092] ; Harbin Science and technology Bureau Foundation[2014RFQXJ119]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000413613900002
出版者	ELSEVIER SCIENCE BV
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29135
专题	系统科学研究所
通讯作者	Chen, Falai
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, KLMM, Beijing 100080, Peoples R China 2.Harbin Inst Technol, Harbin 150001, Heilongjiang, Peoples R China 3.Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China
推荐引用方式 GB/T 7714	Jia, Xiaohong,Shi, Xiaoran,Chen, Falai. Survey on the theory and applications of mu-bases for rational curves and surfaces[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,2018,329:2-23.
APA	Jia, Xiaohong,Shi, Xiaoran,&Chen, Falai.(2018).Survey on the theory and applications of mu-bases for rational curves and surfaces.JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS,329,2-23.
MLA	Jia, Xiaohong,et al."Survey on the theory and applications of mu-bases for rational curves and surfaces".JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 329(2018):2-23.