A Survey of the Representations of Rational Ruled Surfaces*
Yuan Chun-Ming1,2; Perez-Diaz, Sonia3; Shen Li-Yong2
AbstractThe 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.
KeywordBirational transformation characterization implicitization parametrization rational ruled surface reparametrization
Indexed BySCI
Funding ProjectBeijing 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 AreaMathematics
WOS SubjectMathematics, Interdisciplinary Applications
WOS IDWOS:000608140200027
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Document Type期刊论文
Corresponding AuthorShen Li-Yong
Affiliation1.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
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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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