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.

Automated summary

In this paper, the approximation of a circular arc using hexic polynomial curves with 12 contacts is considered. Two methods are presented to obtain Gk approximation curves, where k=3, 4, and these curves interpolate at both endpoints and the midpoint of the circular arc. The approximation curves can be obtained by solving a degree six equation. It is shown that the approximation orders of the methods are 12. The optimal approximation is found for each method and numerical examples are provided to illustrate the approximation orders are 12.