Abstract
A curve interpolation scheme based on piecewise rational quadratic spline is discussed. To preserve the shape of the data, the constraints are made on the free parameters r i , in the description of rational quadratic interpolant. We examine the positivity and/or monotonicity preserving of this rational quadratic interpolant to a given data set. The method easy to used and require less computational steps. The degree of smoothness attained is C 1 Some numerical results will be presented.
An Erratum can be found at http://dx.doi.org/10.1007/978-3-642-05036-7_87
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Butt, S., Brodlie, K.W.: Preserving positivity using piecewise cubic interpolation. Computer Graphics 17(1), 55–64 (1993)
Delbourgo, R., Gregory, J.A.: Shape Preserving piecewise rational interpolation. SIAM J. Stat. Comput. 6, 967–976 (1985a)
Delbourgo, R., Gregory, J.A.: The Determination of Derivative Parameters for a Monotonic Rational Quadratic Interpolant. IMA J. of Numerical Analysis 5, 397–406 (1985b)
Duan, Q., Djidjeli, K., Price, W.G., Twizell, E.H.: Constrained control and approximation properties of a rational interpolating curve. Information Sciences 152, 181–194 (2003)
Fritsch, F.N., Butland, J.: A method for constructing local monotone piecewise cubic interpolants. SIAM J. Sci. and Statist. Comput. 5, 300–304 (1984)
Fritsch, F.N., Carlson, R.E.: Monotone piecewise cubic interpolation. SIAM J. Numer. Anal. 17, 238–246 (1980)
Goodman, T.N.T.: Shape preserving interpolation by curves. In: Levesley, J., Anderson, I.J., Mason, J.C. (eds.) Algorithms for Approximation IV, pp. 24–35. University of Huddersfield Proceedings, Huddersfield (2002)
Gregory, J.A.: Shape preserving spline interpolation. CAD 18(1), 53–57 (1986)
Hussain, M.Z., Ayub, N., Irshad, M.: Visualization of 2D data by rational quadratic functions. Journal of Information and Computing Science 2(1), 17–26 (2007)
Hussain, M.Z., Ali, J.M.: Visualizing positive data by rational quadratic curve. In: 12th Simposium Kebangsaan Sains Matematik (2004)
Kvasov, B.I.: Methods of shape-preserving spline approximation. World Scientific, Singapore (2000)
McAllister, D.F., Roulier, J.A.: An algorithm for computing a shape preserving osculatory quadratic spline. ACM Trans. Math. Software 7, 331–347 (1981)
Passow, E., Roulier, J.A.: Monotone and convex spline interpolation. SIAM J. Numer. Anal. 14, 904–909 (1977)
Sarfraz, M.: Visualization of positive and convex data by a rational cubic spline interpolation. Information Sciences 146, 239–254 (2002)
Sarfraz, M.: A rational cubic spline for the visualization of monotonic data: an alternate approach. Computers & Graphics 27, 107–121 (2003)
Sarfraz, M., Butt, S., Hussain, M.Z.: Visualization of shaped data by a rational cubic spline interpolation. Computer Graphics 25, 833–845 (2001)
Sarfraz, M., Hussain, M.Z., Chaudhry, F.S.: Shape preserving cubic spline for data visualization. Computer Graphics and CAD/CAM 01, 185–193 (2005)
Schmidt, J.W., Heβ, W.: Positivity interpolation with rational quadratic splines. Computing 38, 261-267 (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Karim, S.A.A., Hussain, M.Z. (2009). Retracted: Visualization of Positive and Monotone Data by Rational Quadratic Spline. In: Badioze Zaman, H., Robinson, P., Petrou, M., Olivier, P., Schröder, H., Shih, T.K. (eds) Visual Informatics: Bridging Research and Practice. IVIC 2009. Lecture Notes in Computer Science, vol 5857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-05036-7_41
Download citation
DOI: https://doi.org/10.1007/978-3-642-05036-7_41
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05035-0
Online ISBN: 978-3-642-05036-7
eBook Packages: Computer ScienceComputer Science (R0)