| [1] Dyn N, Levin D, Gregory J A. A 4-point interpolatory subdivision scheme for curve design[J]. Comput.Aided Geomet.Des., 1987, 4:257-268.[2] Hassan M F, Ivrissimitzis I P, Dodgson N A, Sabin M A. An interpolating 4-point C2 ternary stationary subdivision scheme[J]. Comput. Aided Geomet. Des., 2002, 19:1-18.[3] 刘秀平, 李宝军, 苏志勋, 郁博文. 插值细分曲线有理参数点的精确求值[J]. 计算数学, 2009, 31(3):253-260.[4] 邓重阳, 汪国昭. 曲线插值的一种保凸细分方法[J]. 计算机辅助设计与图形学学报, 2009, 21(8):1042-1046.[5] Siddiqi S S, Ahmad N, A new 3-point approximating C2 subdivision scheme[J]. Appl. Math. Lett., 2007, 20:707-711.[6] 张莉, 孙燕, 檀结庆, 时军. 一类新的(2n-1)点二重动态逼近细分[J]. 计算数学, 2017, 39(1):59-69.[7] Maillot J, Stam J. A unified subdivision scheme for polygonal modeling[J]. Comput. Graph. Forum, 2001, 20:471-479.[8] Rossignac J. Education-driven research in CAD[J]. Comput. Aid. Des., 2004, 36:1461-1469.[9] Beccari C V, Casciola G, Romani L. A unified framework for interpolating and approximating univariate subdivision[J]. Appl. Math. Comput., 2010, 216:1169-1180.[10] 亓万锋, 罗钟铉, 樊鑫. 基于逼近型细分的诱导细分格式[J]. 中国科学, 2014, 44(7):755-768.[11] Luo Z X, Qi W F. On interpolatory subdivision from approximating subdivision scheme[J]. Appl. Math. Comput., 2013, 220:339-349.[12] Deng C Y, Ma W Y. A Unified Interpolatory Subdivision Scheme for Quadrilateral Meshes[J]. ACM Trans. Graph., 2013, 32(3):1-11.[13] Levin A. Interpolating nets of curves by smooth subdivision surfaces[J]. ACM SIGGRAPH, 1999:57-64.[14] 王栋, 张曦, 李桂清. 混合细分曲线及其应用[J]. 计算机辅助设计与图形学学报, 2007,19(3):286-291.[15] Pan J, Lin S, Luo X. A combined approximating and interpolating subdivision scheme with C2 continuity[J]. Appl. Math. Lett., 2012, 25:2140-2146.[16] Rehan K, Sabri M A. A combined ternary 4-point subdivision scheme[J]. Appl. Math. Comput., 2016, 276:278-283.[17] Novara P, Romani L. Complete characterization of the regions of C2 and C3 convergence of combined ternary 4-point subdivision schemes[J]. Appl. Math. Lett., 2016, 62:84-91.[18] Lian J A. On a-ary subdivision for curve design:II. 3-point and 5-point interpolatory schemes[J]. Appl. Appl. Math., 2009, 3:176-187.[19] Zheng H C, Hu M, Peng G. Constructing (2n-1)-point ternary interpolatory subdivision schemes by using variation of constants[J]. International Conference on Computational Intelligence and Software Engineering(CISE), 2009, 25(4):1-4.[20] Mustafa G, Ghaffar A, Khan F. The odd-point ternary approximating schemes[J]. Amer. J. Comput. Math., 2011, 1:111-118.[21] Ghaffar A, Mustafa G, Qin K. Unification and application of 3-point approximating subdivision schemes of varying arity[J]. Open J. Appl. Sci., 2012, 2:48-52.[22] Gori L, Pitolli F, Santi E. Refinable ripplets with dilation 3[J]. Jaen J. Approx., 2011, 3:173-191.[23] Gori L, Pitolli F, Santi E. On a class of shape-preserving refinable functions with dilation 3[J]. J. Comput. Appl. Math., 2013, 245:62-74.[24] Hassan M F, Dodgson N A. Ternary and three-point univariate subdivision schemes[J]. In:A. Cohen, J.-L. Merrien, L.L. Schumaker (Eds.), Curve and Surface Fitting:Saint-Malo 2002, Nash-boro Press, 2003, 199-208.[25] Rehan K, Siddiqi S S. A family of ternary subdivision schemes for curves[J]. Appl. Math. Comput., 2015, 270:114-123.[26] Dyn N, Hormann K. Polynomial reproduction by symmetric subdivision schemes[J]. J. Approx. Theory, 2008, 155:28-42.[27] Conti C, Hormann K. Polynomial reproduction for univariate subdivision schemes of any arity[J]. J. Approx. Theory, 2011, 163:413-437.[28] Zheng H C, Ye Z L, Lei Y M, Liu X D. Fractal properties of interpolatory subdivision schemes and their application in fractal generation[J]. Chaos, Soliton. Fract., 2007, 32:113-123.[29] Tan J Q, Zhuang X L, Zhang L. A new four-point shape-preserving C3 subdivision scheme[J]. Comput. Aided Geomet. Des., 2014, 31:57-62.[30] Cao H J, Tan J Q. A binary five-point relaxation subdivision scheme[J]. J. Inf. Comput. Sci., 2013, 10:5903-5910.[31] 檀结庆, 童广悦, 张莉. 基于插值细分的逼近细分法[J]. 计算机辅助设计与图形学学报, 2015,27(7):1162-1166. |
