Approximation of circular arcs by Bezier curves

Abstract

For the circular are of angle 0<alpha<pi we present the explicit form of the best GC(3) quartic approximation and the best GC(2) quartic approximations of various types, and give the explicit form of the Hausdorff distance between the circular are and the approximate Bezier curves for each case. We also show the existence of the GC(4) quintic approximations to the are, and find the explicit form of the best GC(3) quintic approximation in certain constraints and their distances from the are. All approximations we construct in this paper have the optimal order of approximation, twice of the degree of approximate Bezier curves.