Approximation of conic sections by curvature continuous quartic Bezier curves
In this paper we propose two approximation methods of conic section by quartic Bezier curves. These are the extensions of the quartic Bezier approximations of circular arcs presented in Ahn and Kim (1997) [1] and Kim and Ahn (2007) [10] to conic cases. We also give the error bounds of the Hausdorff distances between the conic section and the approximation curves, and show that the error bounds have the approximation order eight. Our methods yield quartic G(2) (curvature) continuous spline approximations of conic sections using the subdivision scheme stated in Floater (1995, 1997) [5,11]. We illustrate our results by some numerical examples. (C) 2010 Elsevier Ltd. All rights reserved.
conic section curvature continuity quartic bezier curve hausdorff distance approximation order spline