KMS Of Academy of mathematics and systems sciences, CAS
| A Survey of the Representations of Rational Ruled Surfaces* | |
| Yuan Chun-Ming1,2; Perez-Diaz, Sonia3; Shen Li-Yong2 | |
| 2021-01-12 | |
| Source Publication | JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
 |
| ISSN | 1009-6124 |
| Pages | 21 |
| Abstract | The rational ruled surface is a typical modeling surface in computer aided geometric design. A rational ruled surface may have different representations with respective advantages and disadvantages. In this paper, the authors revisit the representations of ruled surfaces including the parametric form, algebraic form, homogenous form and Plucker form. Moreover, the transformations between these representations are proposed such as parametrization for an algebraic form, implicitization for a parametric form, proper reparametrization of an improper one and standardized reparametrization for a general parametrization. Based on these transformation algorithms, one can give a complete interchange graph for the different representations of a rational ruled surface. For rational surfaces given in algebraic form or parametric form not in the standard form of ruled surfaces, the characterization methods are recalled to identify the ruled surfaces from them. |
| Keyword | Birational transformation characterization implicitization parametrization rational ruled surface reparametrization |
| DOI | 10.1007/s11424-020-0018-8 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | Beijing Natural Science Foundation[Z190004] ; National Natural Science Foundation of China[61872332] ; University of Chinese Academy of Sciences ; FEDER/Ministerio de Ciencia, Innovacion y Universidades Agencia Estatal de Investigacion[MTM201788796-P] ; Research Group ASYNACS[CCEE2011/R34] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Interdisciplinary Applications |
| WOS ID | WOS:000608140200027 |
| Publisher | SPRINGER HEIDELBERG |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/58019 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Shen Li-Yong |
| Affiliation | 1.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Univ Alcala De Henares, Dept Fis & Matemat, Grp ASYNACS, Alcala De Henares 28871, Spain |
| Recommended Citation GB/T 7714 | Yuan Chun-Ming,Perez-Diaz, Sonia,Shen Li-Yong. A Survey of the Representations of Rational Ruled Surfaces*[J]. JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,2021:21. |
| APA | Yuan Chun-Ming,Perez-Diaz, Sonia,&Shen Li-Yong.(2021).A Survey of the Representations of Rational Ruled Surfaces*.JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY,21. |
| MLA | Yuan Chun-Ming,et al."A Survey of the Representations of Rational Ruled Surfaces*".JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY (2021):21. |
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