Survey on the theory and applications of mu-bases for rational curves and surfaces
文献类型：期刊论文
| 作者 | Jia, Xiaohong1 ; Shi, Xiaoran2; Chen, Falai3
|
| 刊名 | JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
 |
| 出版日期 | 2018-02-01 |
| 卷号 | 329页码:2-23 |
| 关键词 | Rational curve/surface mu-basis Syzygy Parametrization Implicitization Singularity computation |
| ISSN号 | 0377-0427 |
| DOI | 10.1016/j.cam.2017.07.023 |
| 英文摘要 | 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. |
| 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 |
| 语种 | 英语 |
| WOS记录号 | WOS:000413613900002 |
| 出版者 | ELSEVIER SCIENCE BV |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/29134]  |
| 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. |
入库方式： OAI收割
来源：数学与系统科学研究院
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