Abstract Reparametrization of conics can make the parameter as uniform as possible and improve the smoothness at the junction points. The common ways are to use linear rational polynomials or quadratic rational polynomials. In the paper, a cubic rational polynomial is used to reparametrize the conic section, which triples the degree of quadratic rational curve. Experimental results obtained by the parametrization of the circular arcs show that the continuity at the junction point of two circular arcs can reach $C^3$ and the deviation between the parametrization presented in the paper and the arc length parametrization has been reduced about two orders of magnitude, compared with the quadratic rational polynomial parametrization.
Received: 24 February 2014
Published: 08 June 2018
WU Wei-dong, YANG Xun-nian. Cubic rational polynomial parametrization of conics. Applied Mathematics A Journal of Chinese Universities, 2014, 29(4): 419-430.
