Circular arc approximation by hexic polynomial curves

In this paper we consider a circular arc approximation by hexic polynomial curves having 12 contacts with the circular arc. We present two methods for obtaining Gk approximation curves, k = 3, 4, which interpolate at both endpoints and the midpoint of the circular arc. The approximation curves can be obtained by solving an equation of degree six. We show that the approximation orders of our methods are 12. We find the optimal approximation for each method and present numerical examples illustrating that the approximation orders are 12.