The m-Point Quaternary Approximating Subdivision Schemes

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References

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[4] S. S. Siddiqi and M. Younis, “Construction of m-Point Approximating Subdivision Schemes,” Applied Mathematics Letters, Vol. 26, No. 3, 2013, pp. 337-343.
doi:10.1016/j.aml.2012.09.016

[5] 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

[6] M. F. Hassan and N. A. Dodgson, “Ternary and Three Point Univariate Subdivision Schemes,” In: A. Cohen, J.-L. Merrien and L. L. Schumaker, Eds., Curve and Surface Fitting: Sant-Malo, Nashboro Press, Brentwood, 2003, pp. 199-208.

[7] M. F. Hassan, I. P. Ivrissimtzis, N. A. Dodgson and M. A. Sabin, “An Interpolating 4-Point Ternary Stationary Subdivision Scheme,” Computer Aided Geometric Design, Vol. 19, No. 1, 2002, pp. 1-18.
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[8] K. P. Ko, B.-G. Lee and G. J. Yoon, “A Ternary 4-Point Approximating Subdivision Scheme,” Applied Mathematics and Computation, Vol. 190, No. 2, 2007, pp. 1563-1573. doi:10.1016/j.amc.2007.02.032

[9] G. Mustafa, A. Ghaffar and F. Khan, “The Odd-Point Ternary Approximating Schemes,” American Journal of Computational Mathematics, Vol. 1, No. 2, 2011, pp. 111-118.

[10] S. R. Buss, “3-D Computer Graphics A Mathematical Introduction with OpenGL,” 1st Edition, Cambridge University Press, New York, 2003.
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[11] Y. Tang, K. P. Ko and B. G. Lee, “A New Proof of the Smoothness of 4-Point Deslauriers-Dubuc Scheme,” Journal of Applied Mathematics and Computing Vol. 18, No. 1-2, 2005, pp. 553-562.

[12] C. Conti and K. Hormann, “Polynomial Reproduction for Univariate Subdivision Schemes of any Arity,” Journal of Approximation Theory, Vol. 163, No. 4, 2011, pp. 413-437. doi:10.1016/j.jat.2010.11.002