×
Duan, Qi; Djidjeli, K.; Price, W. G.; Twizell, E. H.

Weighted rational cubic spline interpolation and its application. (English) Zbl 0961.65009

J. Comput. Appl. Math. 117, No. 2, 121-135 (2000).
A weighted rational cubic spline is derived by taking a linear combination of the rational cubic spline with linear denominator and the rational cubic spline based on function values. A sufficient condition for the weighted rational spline curve to lie between two given piecewise linear curves is given. How well the weighted interpolation function approximates the function being interpolated is studied also. Various numerical examples are presented.
Reviewer: N.Ţăndăreanu (Craiova)

Cited in 16 Documents

MSC:

65D05 Numerical interpolation
65D07 Numerical computation using splines
41A20 Approximation by rational functions

Keywords:

rational spline; cubic spline; constrained interpolation; weighted rational interpolation; numerical examples
Cite Review PDF
Full Text: DOI

References:

[1] Boehm, W.; Farin, G.; Kahmann, J., A survey of curve and surface methods, Comput. Aided Geom. Des., 1, 1-60 (1984) · Zbl 0604.65005
[2] Dierckx, P.; Tytgat, B., Generating the Bézier points of \(β\)-spline curve, Comput. Aided Geom. Des., 6, 279-291 (1989) · Zbl 0682.65004
[3] Duan, Q.; Djidjeli, K.; Price, W. G.; Twizell, E. H., Rational cubic spline based on function values, Comput. Graph, 22, 4, 479-486 (1998)
[5] Duan, Q.; Wang, X.; Cheng, F., Constrained interpolation using rational cubic spline curve with linear denominators, Korean J. Comput. Appl. Math., 6, 1, 203-215 (1999) · Zbl 0955.65005
[6] Foley, T. A., Local Control of Interval Tension Using Weighted Splines, Comput. Aided Geom. Des., 3, 281-294 (1986) · Zbl 0645.65007
[8] Gregory, J. A.; Sarfraz, M.; Yuen, P. K., Interactive curve design using \(C^2\) rational splines, Comput. Graph, 18, 2, 153-159 (1994)
[10] Nielson, G. M., Rectangular \(ν\)-splines, IEEE Comput. Graph. Appl., 6, 35-40 (1986)
[12] Piegl, L., On NURBS: a survey, IEEE Comput. Graphics Appl., 11, 5, 55-71 (1991)
[13] Sarfraz, M., Interpolatory rational cubic spline with biased, point and interval tension, Comput. Graph., 16, 4, 427-430 (1992)
[14] Schmidt, J. W.; Hess, W., Positive interpolation with rational quadratic splines, Computing, 38, 261-267 (1987) · Zbl 0676.41017
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.