Some new G1 quartic parametric approximants of circular arcs

In this paper a method for approximation of circular arc by quartic Bézier curve is presented. Interpolation by geometrically continuous (G1) parametric polynomials is considered and necessary and sufficient conditions for the existence of the solution are established. Optimal asymptotic approximation order eight is also confirmed for the obtained approximant. Application of our new solution to approximation of conic sections is presented and some numerical examples provided.