Taylor theorem for planar curves
HTML articles powered by AMS MathViewer
- by Abedallah Rababah PDF
- Proc. Amer. Math. Soc. 119 (1993), 803-810 Request permission
Abstract:
We describe an approximation method for planar curves that significantly improves the standard rate obtained by local Taylor approximations. The method exploits the freedom in the choice of the parametrization and achieves the order $4m/3$ where $m$ is the degree of the approximating polynomial parametrization. Moreover, we show for a particular set of curves that the optimal rate $2m$ is possible.References
-
W. Beohm, G. Farin, and J. Kahmann, A survey of curve and surface methods in $CAGD$, Computer Aided Geometric Design 1 (1984), 1-60.
- Carl de Boor, Klaus Höllig, and Malcolm Sabin, High accuracy geometric Hermite interpolation, Comput. Aided Geom. Design 4 (1987), no. 4, 269–278. MR 937366, DOI 10.1016/0167-8396(87)90002-1
- Tor Dokken, Morten Dæhlen, Tom Lyche, and Knut Mørken, Good approximation of circles by curvature-continuous Bézier curves, Comput. Aided Geom. Design 7 (1990), no. 1-4, 33–41. Curves and surfaces in CAGD ’89 (Oberwolfach, 1989). MR 1074597, DOI 10.1016/0167-8396(90)90019-N
- Gerald Farin, Curves and surfaces for computer aided geometric design, Computer Science and Scientific Computing, Academic Press, Inc., Boston, MA, 1988. A practical guide; With contributions by P. Bézier and W. Boehm. MR 974109
- Michael Goldapp, Approximation of circular arcs by cubic polynomials, Comput. Aided Geom. Design 8 (1991), no. 3, 227–238. MR 1122918, DOI 10.1016/0167-8396(91)90007-X
- T. N. T. Goodman and K. Unsworth, Shape preserving interpolation by curvature continuous parametric curves, Comput. Aided Geom. Design 5 (1988), no. 4, 323–340. MR 983466, DOI 10.1016/0167-8396(88)90012-X
- Josef Hoschek and Dieter Lasser, Grundlagen der geometrischen Datenverarbeitung, B. G. Teubner, Stuttgart, 1989 (German). MR 1055828, DOI 10.1007/978-3-322-99494-3 K. Höllig, Algorithms for rational spline curves, Conference on Applied Mathematics and Computing, ARO Report 88-1, 1988. S. Pumm, Interpolation an "zu vielen" Punkten, Diplomarbeit, Mathematisches Institut A, Stuttgart Universität, Pfaffenwaldring 57, 7000 Stuttgart 80, Germany, 1990. A. Rababah, Approximation von Kurven mit Polynomen und Splines, Ph.D. Thesis, Mathematisches Institut A, Universität Stuttgart, Pfaffenwaldring 57, D-7000 Stuttgart 80, Germany, 1992. —, High accuracy piecewise approximation for planar curves, J. Approx. Theory (to appear).
- Abedallah Rababah, High order approximation method for curves, Comput. Aided Geom. Design 12 (1995), no. 1, 89–102. MR 1311120, DOI 10.1016/0167-8396(94)00004-C —, Hermite approximation with high accuracy, Constr. Approx. (to appear).
- Thomas W. Sederberg and Masanori Kakimoto, Approximating rational curves using polynomial curves, NURBS for curve and surface design (Tempe, AZ, 1990) SIAM, Philadelphia, PA, 1991, pp. 149–158. MR 1133471
- Fujio Yamaguchi, Curves and surfaces in computer aided geometric design, Springer-Verlag, Berlin, 1988. Translated from the Japanese by Harold Solomon. MR 971750, DOI 10.1007/978-3-642-48952-5
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 803-810
- MSC: Primary 41A58; Secondary 41A10
- DOI: https://doi.org/10.1090/S0002-9939-1993-1151815-2
- MathSciNet review: 1151815