A Survey of the Representations of Rational Ruled Surfaces*

doi:10.1007/s11424-020-0018-8

CSpace

	A Survey of the Representations of Rational Ruled Surfaces*
	Yuan Chun-Ming 1,2; Perez-Diaz, Sonia 3; Shen Li-Yong 2
	2021-01-12
发表期刊	JOURNAL OF SYSTEMS SCIENCE & COMPLEXITY
ISSN	1009-6124
页码	21
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.
关键词	Birational transformation characterization implicitization parametrization rational ruled surface reparametrization
DOI	10.1007/s11424-020-0018-8
收录类别	SCI
语种	英语
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
WOS类目	Mathematics, Interdisciplinary Applications
WOS记录号	WOS:000608140200027
出版者	SPRINGER HEIDELBERG
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/58019
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.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
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.