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http://dx.doi.org/10.12941/jksiam.2013.17.171

CIRCLE APPROXIMATION BY QUARTIC G2 SPLINE USING ALTERNATION OF ERROR FUNCTION  

Kim, Soo Won (DEPARTMENT OF MATHEMATICS EDUCATION, CHOSUN UNIVERSITY)
Ahn, Young Joon (DEPARTMENT OF MATHEMATICS EDUCATION, CHOSUN UNIVERSITY)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.17, no.3, 2013 , pp. 171-179 More about this Journal
Abstract
In this paper we present a method of circular arc approximation by quartic B$\acute{e}$zier curve. Our quartic approximation method has a smaller error than previous quartic approximation methods due to the alternation of the error function of our quartic approximation. Our method yields a closed form of error so that subdivision algorithm is available, and curvature-continuous quartic spline under the subdivision of circular arc with equal-length until error is less than tolerance. We illustrate our method by some numerical examples.
Keywords
circular arc; quartic B$\acute{e}$zier curve; spline; Hausdorff distance; approximation order; geometric contact;
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1 Y. J. Ahn. Approximation of conic sections by curvature continuous quartic Bezier curves. Comp. Math. Appl., 60:1986-1993, 2010.   DOI   ScienceOn
2 Y. J. Ahn and H. O. Kim. Approximation of circular arcs by Bezier curves. J. Comp. Appl. Math., 81:145-163, 1997.   DOI   ScienceOn
3 T. Dokken, M. Daehlen, T. Lyche, and K. Morken. Good approximation of circles by curvature-continuous bezier curves. Comp. Aided Geom. Desi., 7:33-41, 1990.   DOI   ScienceOn
4 L. Fang. Circular arc approximation by quintic polynomial curves. Comp. Aided Geom. Desi., 15:843-861, 1998.   DOI   ScienceOn
5 L. Fang. $G^{3}$ approximation of conic sections by quintic polynomial. Comp. Aided Geom. Desi., 16:755-766, 1999.   DOI   ScienceOn
6 M. Floater. High-order approximation of conic sections by quadratic splines. Comp. Aided Geom. Desi., 12(6):617-637, 1995.   DOI   ScienceOn
7 M. Floater. An O($h^{2n}$) Hermite approximation for conic sectoins. Comp. Aided Geom. Desi., 14:135-151, 1997.   DOI   ScienceOn
8 M. Goldapp. Approximation of circular arcs by cubic polynomials. Comp. Aided Geom. Desi., 8:227-238, 1991.   DOI   ScienceOn
9 S. Hur and T. Kim. The best $G^{1}$ cubic and $G^{2}$ quartic Bezier approximations of circular arcs. J. Comp. Appl. Math., 236:1183-1192, 2011.   DOI   ScienceOn
10 S. H. Kim and Y. J. Ahn. Approximation of circular arcs by quartic bezier curves. Comp. Aided Desi., 39(6):490-493, 2007.   DOI   ScienceOn
11 I. K. Lee, M. S. Kim, and G. Elber. Planar curve offset based on circle approximation. Comp. Aided Desi., 28:617-630, 1996.   DOI   ScienceOn
12 Z. Liu, J. Tan, X. Chen, and L. Zhang. An approximation method to circular arcs. Appl. Math. Comp., 15:1306-1311, 2012.
13 K. Morken. Best approximation of circle segments by quadratic Bezier curves. In P.J. Laurent, A. Le Mehaute, and L.L. Schumaker, editors, Curves and Surfaces, pages 387-396. Academic Press, 1990.