Shape Preservation of the Stationary 4-Point Quaternary Subdivision Schemes
In this paper, the shape preserving properties of the stationary 4-point quaternary approximating and interpolating subdivision schemes of Ko  are fully investigated. We will analyzed what conditions should be introduced on the initial control points so that the limit curve achieved by the subdivision schemes presented in  are both monotonicity and convexity preserving. Conclusively the whole discussion is followed by examples.
G. Akram, K. Bibi, K. Rehan and S.S. Siddiqi, Shape preservation of 4-point interpolating nonstationary subdivision scheme, Journal of Computational and Applied Mathematics 319 (2017), 480 – 492, DOI: 10.1016/j.cam.2017.01.026.
S. Amat, R. Donat and J.C. Trillo, Proving convexity preserving properties of interpolatory subdivision schemes through reconstruction operators, Applied Mathematics and Computation 219 (2013), 7413 – 7421, DOI: 10.1016/j.amc.2013.01.024.
P. Ashraf and G. Mustafa, A generalized non-stationary 4-point b-ary approximating scheme, British Journal of Mathematics & Computer Science 4 (2014), 104, DOI: 10.9734/bjmcs/2014/4120.
C. Beccari, G. Casciola and L. Romani, An interpolating 4-point C2 ternary non-stationary subdivision scheme with tension control, Computer Aided Geometric Design 24 (2007), 210 – 219, DOI: 10.1016/j.cagd.2007.02.001.
Z. Cai, Convexity preservation of the interpolating four-point C2 ternary stationary subdivision scheme, Computer Aided Geometric Design 26 (2009), 560 – 565, DOI: 10.1016/j.cagd.2009.02.004.
F. Dyn, F. Kuijt, D. Levin and R. van Damme, Convexity preservation of the four-point interpolatory subdivision scheme, Computer Aided Geometric Design 16 (1999), 789 – 792, DOI: 10.1016/s0167- 8396(99)00019-9.
N. Dyn, D. Levin and J.A. Gregory, A 4-point interpolatory subdivision scheme for curve design, Computer Aided Geometric Design 4 (1987), 257 – 268, DOI: 10.1016/0167-8396(87)90001-x.
M.F. Hassan, I. Ivrissimitzis, N.A. Dodgson and M.A. Sabin, An interpolating 4-point C2 ternary stationary subdivision scheme, Computer Aided Geometric Design 19 (2002), 1 – 18, DOI: 10.1016/s0167-8396(01)00084-x.
K.-P. Ko, Quatnary approximating 4-point subdivision scheme, Journal of the Korea Society for Industrial and Applied Mathematics 13 (2009), 307 – 314, https://portal.koreascience.or.kr/article/articleresultdetail.jsp?no=E1TAAE_2009_v13n4_307.
G. Mustafa and P. Ashraf, A new 6-point ternary interpolating subdivision scheme, Journal of Information and Computing Science 5 (2010), 199 – 210.
S.S. Siddiqi and T. Noreen, Convexity preservation of six point C2 interpolating subdivision scheme, Applied Mathematics and Computation 265 (2015), 936 – 944, DOI: 10.1016/j.amc.2015.04.024.
J. Tan, B. Wang and J. Shi, A five-point subdivision scheme with two parameters and a four-point shape-preserving scheme, Mathematical and Computational Applications 22 (2017), 22, DOI: 10.3390/mca22010022.
J. Tan, Y. Yao, H. Cao and L. Zhang, Convexity preservation of five-point binary subdivision scheme with a parameter, Applied Mathematics and Computation 245 (2014), 279 – 288, DOI: 10.1016/j.amc.2014.07.071.
C. Zhijie, Four-point scheme and convex-preserving algorithm, Journal of Computer Aided Design & Computer Graphics 6(1) (1994), 33 – 36 (in Chinese), http://en.cnki.com.cn/Article_en/ CJFDTOTAL-JSJF401.005.htm.
- There are currently no refbacks.
eISSN 0975-8607; pISSN 0976-5905