On optimal polynomial geometric interpolation of circular arcs according to the Hausdorff distance

The problem of the optimal approximation circular arcs by parametric polynomial curves is considered. optimality relates to Hausdorff distance and have not been studied yet in literature. Parametric low degree are used a geometric continuity prescribed at boundary points arc. A general theory about existence uniqueness approximant presented rigorous analysis done for some special cases which curve order smoothness differ two. This includes practically interesting parabolic $G^0$, cubic $G^1$, quartic $G^2$ quintic $G^3$ interpolation. Several numerical examples confirm theoretical results.