A Survey of the Representations of Rational Ruled Surfaces  

作　　者：YUAN Chun-Ming PEREZ-DIAZ Sonia SHEN Li-Yong 

机构地区：[1]KLMM,Academy of Mathematics and Systems Sciences,Chinese Academy of Sciences,Beijing 100190,China [2]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China [3]Grupo ASYNACS,Dpto.de Fisica y Matematicas,Universidad de Alcala,28871-Alcala de Henares,Madrid,Spain

出　　处：《Journal of Systems Science & Complexity》2021年第6期2357-2377,共21页系统科学与复杂性学报（英文版）

基　　金：supported by Beijing Natural Science Foundation under Grant No.Z190004;the National Natural Science Foundation of China under Grant No.61872332;the University of Chinese Academy of Sciences and by FEDER/Ministerio de Ciencia;Innovación y Universidades Agencia Estatal de Investigación/MTM2017-88796-P(Symbolic Computation:New challenges in Algebra and Geometry together with its applications);the Research Group ASYNACS(Ref.CCEE2011/R34)。

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 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]