Back
 AJCM  Vol.3 No.3 , September 2013
A Family of 4-Point n-Ary Interpolating Scheme Reproducing Conics
Abstract: The n-ary subdivision schemes contrast favorably with their binary analogues because they are capable to produce limit functions with the same (or higher) smoothness but smaller support. We present an algorithm to generate the 4-point n-ary non-stationary scheme for trigonometric, hyperbolic and polynomial case with the parameter for describing curves. The performance, analysis and comparison of the 4-point ternary scheme are also presented.
Cite this paper: M. Bari and G. Mustafa, "A Family of 4-Point n-Ary Interpolating Scheme Reproducing Conics," American Journal of Computational Mathematics, Vol. 3 No. 3, 2013, pp. 217-221. doi: 10.4236/ajcm.2013.33031.
References

[1]   M. K. Jena, P. Shunmugaraj and P. C. Das, “A Non-Stationary Subdivision Scheme for Curve Interpolation,” ANZIAM Journal, Vol. 44, No. E, 2003, pp. 216-235.

[2]   J. Yoon, “Analysis of Non-Stationary Interpolatory Subdivision Schemes Based on Exponential Polynomials,” Geometric Modeling and Processing, Vol. 4077, 2006, pp. 563-570.

[3]   C. Beccari, G. Casciola and L. Romani, “A Non-Stationary Uniform Tension Controlled Interpolating 4-Point Scheme Reproducing Conics,” Computer Aided Geometric Design, Vol. 24, No. 1, 2007, pp. 1-9. doi:10.1016/j.cagd.2006.10.003

[4]   S. Daniel and P. Shunmugaraj, “Some Interpolating Non-Stationary Subdivision Schemes,” International Symposium on Computer Science and Society, Kota Kinabalu, 16-17 July 2011, pp. 400-403. doi:10.1109/ISCCS.2011.110

[5]   G. Deslauriers and S. Dubuc, “Symmetric Iterative Interpolation Processes,” Constructive Approximation, Vol. 5, No. 1, 1989, pp. 49-68. doi:10.1007/BF01889598

[6]   N. Dyn and D. Levin, “Analysis of Asymptotically Equivalent Binary Subdivision Schemes,” Journal of Mathematical Analysis and Applications, Vol. 193, No. 2, 1995, pp. 594-621. doi:10.1006/jmaa.1995.1256

[7]   N. Dyn and D. Levin, “Subdivision Schemes in Geometric Modelling,” Acta Numerica, Vol. 11, 2002, pp. 73-144. doi:10.1017/S0962492902000028

[8]   R. Klen, M. Lehtonen and M. Vuorinen, “On Jordan Type Inequalities for Hyperbolic Functions,” Journal of Inequalities and Applications, Vol. 2010, 2010, Article ID: 362548.

 
 
Top