References

Abbas, M., 2012. Shape preserving data visualization for curves and surfaces using rational cubic functions. Ph.D Thesis, Universiti Sains Malaysia (USM), Penang, Malaysia.

Abbas, M., A.A. Majid, M.N.H. Awang and J.M. Ali, 2012. Constrained shape preserving rational bi-cubic spline interpolation. World Appl. Sci. J., 20: 790-800.
CrossRef  |  

Abdul Karim, S.A., K.V. Pang and A. Saaban, 2015. Positivity preserving interpolation using rational bicubic spline. J. Appl. Math., Vol. 2015. 10.1155/2015/572768

Beliakov, G., 2005. Monotonicity preserving approximation of multivariate scattered data. BIT Numer. Math., 45: 653-677.
CrossRef  |  Direct Link  |  

Carlson, R.E. and F.N. Fritsch, 1985. Monotone piecewise bicubic interpolation. SIAM. J. Numer. Anal., 22: 386-400.
CrossRef  |  Direct Link  |  

Casciola, G. and L. Romani, 2003. Rational Interpolants with Tension Parameters. In: Curve and Surface Design: Saint-Malo 2002, Cohen, A., J.L. Merrien and L.L. Schumaker (Eds.). Nashboro Press Brentwood, Tennessee, pp: 41-50.

Costantini, P., 1997. Boundary-valued shape-preserving interpolating splines. ACM. Trans. Math. Software, 23: 229-251.
CrossRef  |  Direct Link  |  

Duan, Q., H. Zhang, Y. Zhang and E.H. Twizell, 2006. Bounded property and point control of a bivariate rational interpolating surface. Comput. Math. Appl., 52: 975-984.
CrossRef  |  Direct Link  |  

Duan, Q., L. Wang and E.H. Twizell, 2004. A new bivariate rational interpolation based on function values. Inf. Sci., 166: 181-191.
CrossRef  |  Direct Link  |  

Farin, G., 2002. Curves and Surfaces for CAGD: A Practical Guide. 5th Edn., Academic Press, San Francisco, ISBN: 978-1-55860-737-8.

Hussain, M., M.Z. Hussain, A. Waseem and M. Javaid, 2015. $$\hbox {GC}^{1}$$GC1 shape-preserving trigonometric surfaces. J. Math. Imaging Vision, 53: 21-41.
CrossRef  |  Direct Link  |  

Hussain, M.Z. and M. Hussain, 2007. Visualization of data preserving monotonicity. Applied Math. Comput., 190: 1353-1364.
CrossRef  |  Direct Link  |  

Hussain, M.Z., M. Hussain and A. Waseem, 2014. Shape-preserving trigonometric functions. Comput. Appl. Math., 33: 411-431.
Direct Link  |  

Hussain, M.Z., M. Hussain and M. Amjad, 2012. Shape preserving rational bi-cubic function. Egypt. Inf. J., 13: 147-154.
Direct Link  |  

Hussain, M.Z., M. Sarfraz and T.S. Shaikh, 2012. Monotone data visualization using rational functions 1. World Appl. Sci. J., 16: 1496-1508.
Direct Link  |  

Ibraheem, F., M. Hussain, M.Z. Hussain and A.A. Bhatti, 2012. Positive data visualization using trigonometric function. J. Appl. Math., 2012: 1-19.
Direct Link  |  

Karim, S.A.A. and V.P. Kong, 2014. Monotonicity-preserving using rational cubic spline interpolation. Res. J. Appl. Sci., 9: 214-223.
CrossRef  |  Direct Link  |  

Karim, S.A.A., 2017. Rational cubic spline for shape preserving interpolation. Ph.D Thesis, Universiti Sains Malaysia, Malaysia.

Liu, X., Y. Zhu and S. Liu, 2014. Positivity and monotonicity preserving biquartic rational interpolation spline surface. J. Appl. Math., 2014: 1-11.
CrossRef  |  Direct Link  |  

Stewart, J., 2012. Calculus Metric. 7th Edn., Brooks/Cole Publishing Company, Pacific Grove, California, USA.,.

Wang, Q. and J. Tan, 2006. Shape preserving piecewise rational biquartic surface. J. Inf. Comput. Sci., 3: 295-302.
Direct Link  |