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 au...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.展开更多
基金supported by Beijing Natural Science Foundation under Grant No.Z190004the National Natural Science Foundation of China under Grant No.61872332+2 种基金the University of Chinese Academy of Sciences and by FEDER/Ministerio de CienciaInnovación 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)。
文摘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.
