APPROXIMATION ORDER OF C 3 QUARTIC B-SPLINE APPROXIMATION OF CIRCULAR ARC

Abstract

In this paper, we present a C 3 quartic B-spline approximation of circular arcs. The Hausdorff distance between the C 3 quartic B-spline curve and the circular arc is obtained in closed form. Using this error analysis, we show that the approximation order of our approximation method is six. For a given circular arc and error tolerance we find the C 3 quartic B-spline curve having the minimum number of control points within the tolerance. The algorithm yielding the C 3 quartic B-spline approximation of a circular arc is also presented.