A Survey of the Representations of Rational Ruled Surfaces*

doi:10.1007/s11424-020-0018-8

	A Survey of the Representations of Rational Ruled Surfaces*
	Yuan Chun-Ming 2,3; Perez-Diaz, Sonia 1; Shen Li-Yong 3
刊名	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
	2021-01-12
页码	21
关键词	Birational transformation characterization implicitization parametrization rational ruled surface reparametrization
ISSN号	1009-6124
DOI	10.1007/s11424-020-0018-8
英文摘要	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.
资助项目	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研究方向	Mathematics
语种	英语
出版者	SPRINGER HEIDELBERG
WOS记录号	WOS:000608140200027
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/58018]
专题	中国科学院数学与系统科学研究院
通讯作者	Shen Li-Yong
作者单位	1.Univ Alcala De Henares, Dept Fis & Matemat, Grp ASYNACS, Alcala De Henares 28871, Spain 2.Chinese Acad Sci, Acad Math & Syst Sci, KLMM, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
推荐引用方式 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.