An approximation method for convolution curves of regular curves and ellipses

In this paper, we present a method of $G^2$ Hermite interpolation of convolution curves of regular plane curves and ellipses. We show that our approximant is also a $C^1$ Hermite interpolation of the convolution curve. This method yields a polynomial curve if the trajectory curve is a polynomial curve. Our approximation method is applied to two previous numerical examples. The results of our method are compared with those of previous methods, and the merits and demerits are analyzed. Compared with previous methods, the merits of our method are that the approximant is $G^2$ and $C^1$ Hermite interpolation, and the degree of the approximant or the required number of segments of the approximant within error tolerances is small.