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Survey on the theory and applications of mu-bases for rational curves and surfaces
Jia, Xiaohong1; Shi, Xiaoran2; Chen, Falai3
2018-02-01
Source PublicationJOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
ISSN0377-0427
Volume329Pages:2-23
Abstractmu-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.
KeywordRational curve/surface mu-basis Syzygy Parametrization Implicitization Singularity computation
DOI10.1016/j.cam.2017.07.023
Language英语
Funding ProjectNSFC[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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000413613900002
PublisherELSEVIER SCIENCE BV
Citation statistics
Cited Times:3[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29135
Collection系统科学研究所
Affiliation1.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
Recommended Citation
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.
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