Investigation of practical representation and parameterization of the rational cubic conic sections

Abstract

This paper presents a practical representation containing a parameter of rational cubic conic sections and researchs deeply the inner properties. Firstly,The parameter how to affect the control points, inner weights and shoulder point is discussed. Secondly,the inner relation between the parameter and the weights of the nonstandard-form quadratic rational conic sections is analysed in detail. Change in the parameter value actually corresponds to a rational linear parameter transformation. Finally, we discuss the inverse calculation of the cubic rational conic sections and obtain the inverse calculation methods suitable for engineering applications. DOI: http://dx.doi.org/10.11591/telkomnika.v11i1.1863