Visualization of positive and convex data by a rational cubic spline interpolation

Information Sciences

Volumn 146, Issue 1-4, 2002, Pages 239-254

  Sarfraz, Muhammad ^a  

^a KING FAHD UNIVERSITY OF PETROLEUM AND MINERALS   (Saudi Arabia)

Author keywords

Convex; Data visualization; Interpolation; Positive; Rational spline

Indexed keywords

COMPUTER GRAPHICS; COMPUTER SIMULATION; CONSTRAINT THEORY; DATA STRUCTURES; FUNCTIONS; INFORMATION ANALYSIS; INTERPOLATION; VISUALIZATION;

CONVEX DATA SETS; DATA VISUALIZATION;

DATA REDUCTION;

EID: 0036798797     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-0255(02)00209-8     Document Type: Article

References (16)

1. McAllister D.F., Roulier J.A. An algorithm for computing a shape preserving oscillatory quadratic spline. ACM Trans. Math. Software. 7:1981;331-347.
2. Passow E., Roulier J.A. Monotone and convex spline interpolation. SIAM J. Numer. Anal. 14:1977;904-909.
3. Fritsch F.N., Carlson R.E. Monotone piecewise cubic interpolation. SIAM J. Numer. Anal. 17:1980;238-246.
4. Gregory J.A. Shape preserving spline interpolation. Comput. Aided Des. 18(1):1986;53-57.
5. Fritsch F.N., Butland J. A method for constructing local monotone piecewise cubic interpolants. SIAM J. Sci. Stat. Comput. 5:1984;303-304.
6. Schumaker L.L. On shape preserving quadratic spline interpolation. SIAM J. Numer. Anal. 20:1983;854-864.
7. Brodlie K.W., Butt S. Preserving convexity using piecewise cubic interpolation. Comput. Graphics. 15:1991;15-23.
8. Butt S., Brodlie K.W. Preserving positivity using piecewise cubic interpolation. Comput. Graphics. 17(1):1993;55-64.
9. Sarfraz M. Convexity preserving piecewise rational interpolation for planar curves. Bull. Korean Math. Soc. 29(2):1992;193-200.
10. Sarfraz M. Preserving monotone shape of the data using piecewise rational cubic functions. Comput. Graphics. 21(1):1997;5-14.
11. Brodlie K.W. Methods for drawing curves. Earnshaw R.A. Fundamental Algorithm for Computer Graphics. 1985;303-323 Springer, Berlin/Heidelberg.
12. DeVore A., Yan Z. Error analysis for piecewise quadratic curve fitting algorithms. Comput. Aided Geom. Des. 3:1986;205-215.
13. Greiner K. A survey on univariate data interpolation and approximation by splines of given shape. Math. Comput. Model. 15:1991;97-106.
14. Lahtinen A. Monotone interpolation with application to estimation of taper curves. Ann. Numer. Math. 3:1996;151-161.
15. Sarfraz M. Interpolatory rational cubic spline with biased, point and interval tension. Comput. Graphics. 16(4):1992;427-430.
16. Sarfraz M. A rational cubic spline for the visualization of monotonic data. Comput. Graphics. 24(4):2000;509-516.