Approximation of circular arcs by Bézier curves

For the circular arc of angle 0<α<π we present the explicit form of the best GC3 quartic approximation and the best GC2 quartic approximations of various types, and give the explicit form of the Hausdorff distance between the circular arc and the approximate Bézier curves for each case. We also show the existence of the GC4 quintic approximations to the arc, and find the explicit form of the best GC3 quintic approximation in certain constraints and their distances from the arc. All approximations we construct in this paper have the optimal order of approximation, twice of the degree of approximate Bézier curves.