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Scientific Data Visualization with Shape Preserving C1 Rational Cubic Interpolation

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Abstract (2. Language): 
This paper deals with the shape preserving C1 rational cubic interpolation. The developed rational cubic interpolating function has only one free parameter. The approximation order of rational cubic function is investigated and range of optimal error constant is determined. Moreover, positive, constrained and monotone data preserving schemes are developed.
194-212

REFERENCES

References: 

[1] Akima, H., A new method of interpolation and smooth curve fitting based on local
procedures, Journal of the Association for Computing Machinery, 17, (1970), 589-602.
[2] Beliakov, G., Monotonicity preserving approximation of multivariate scattered data, BIT,
45(4), (2005), 653-677.
[3] Butt, S. and Brodlie, K. W., Preserving positivity using piecewise cubic interpolation,
Computers and Graphics, 17(1), (1993), 55-64.
[4] Duan, Q., Zhang, H., Zhang, Y. and Twizell, E. H., Error estimation of a kind of rational
spline, Journal of Computational and Applied Mathematics, 200(1), (2007), 1-11.
[5] Fahr, R. D. and Kallay, M., Monotone linear rational spline interpolation, Computer Aided
Geometric Design, 9, (1992), 313-319.
[6] Gerald, C. F. and Wheatley, P. O., Applied Numerical Analysis, 7th Edition, Addison
Wesley Publishing Company, (2003).
[7] Goodman, T. N. T., Ong, B. H. and Unsworth, K., Constrained interpolation using rational
cubic splines, Proceedings of NURBS for Curve and Surface Design, G. Farin (eds),
(1991), 59-74.
[8] Goodman, T. N. T., Shape preserving interpolation by curves, Proceeding of Algorithms
for Approximation IV, J. Levesley, I. J. Anderson and J. C. Mason(eds.), University of
Huddersfeld, (2002), 24-35.
[9] Hussain, M. Z. and Hussain, M., Visualization of data preserving monotonicity, Applied
Mathematics and Computation, 190, (2007), 1353-1364.
[10] Hussain, M. Z. and Sarfraz, M., Positivity-preserving interpolation of positive data by
rational cubics, Journal of Computational and Applied Mathematics, 218(2), (2008),
446-458.
[11] Hussain, M. Z. and Sarfraz, M., Monotone piecewise rational cubic interpolation, To be
appeared in International Journal of Computer Mathematics, 86, (2009).
[12] Lamberti, P. and Manni, C., Shape-preserving functional interpolation via parametric
cubics, Numerical Algorithms, 28, (2001), 229-254.
[13] Sarfraz, M., Butt, S. and Hussain, M. Z., Visualization of shaped data by a rational cubic
spline interpolation, Computers and Graphics, 25(5), (2001), 833-845.
[14] Sarfraz, M., Hussain, M. Z. and Chaudhry, F. S., Shape preserving cubic spline for data
visualization, Computer Graphics and CAD/CAM, 01, (2005), 189-193.
[15] Schmidt, J. W. and Hess, W., Positivity of cubic polynomial on intervals and positive
spline interpolation, BIT, 28, (1988), 340-352.
[16] Schultz, M. H., Spline Analysis, Prentice-Hall, Englewood Cliffs, New Jersey, (1973).

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