An approximation of circular arcs by quartic Bezier curves

In this paper we propose an approximation method for circular arcs by quartic Bezier curves. Using an alternative error function, we give the closed form of the Hausdorff distance between the circular arc and the quartic Bezier curve. We also show that the approximation order is eight. By subdivision of circular arcs with equi-length, our method yields the curvature continuous spline approximation of the circular arc. We confirm that the approximation proposed in this paper has a smaller error than previous quartic Bezier approximations. (C) 2007 Elsevier Ltd. All rights reserved.