计算数学
       首页 |  期刊介绍 |  编委会 |  投稿指南 |  期刊订阅 |  下载中心 |  留言板 |  联系我们 |  重点论文 |  在线办公 | 
计算数学  2019, Vol. 41 Issue (4): 367-380    DOI:
论文 最新目录 | 下期目录 | 过刊浏览 | 高级检索 Previous Articles  |  Next Articles  
一类融合逼近和插值的曲线细分
马欢欢, 张莉, 唐烁, 檀结庆
合肥工业大学数学学院, 合肥 230009
A CLASS OF COMBINED APPROXIMATING AND INTERPOLATING SUBDIVISION FOR CURVES
Ma Huanhuan, Zhang Li, Tang Shuo, Tan Jieqing
School of Mathematics, Hefei University of Technology, Hefei 230009, China
 全文: PDF (668 KB)   HTML (1 KB)   输出: BibTeX | EndNote (RIS)      背景资料
摘要 采用生成多项式为主的方法对一类融合逼近和插值三重细分格式的支撑区间、多项式生成、连续性、多项式再生及分形性质进行了分析,给出并证明了极限曲线Ck连续的充分条件.通过对融合型细分规则中参数变量的适当选择来实现对极限曲线的形状调整,从而衍生出具有良好性质的新格式,并将这类新格式与现有格式进行比较.数值实例表明这类新格式生成的极限曲线具有较好的保形性.
服务
把本文推荐给朋友
加入我的书架
加入引用管理器
E-mail Alert
RSS
作者相关文章
关键词多项式生成性   连续性   多项式再生性   分形     
Abstract: Some properties of a combined approximating and interpolating ternary subdivision scheme, such as support, continuity and fractal property, are analyzed by means of the Laurent polynomials. The sufficient conditions of Ck continuity properties are proved. It is pointed out that the parameter can be adjusted to control the shape of the limit curve, which generates brand-new ternary schemes, and some comparisons with other methods are given. Examples show that this new family of schemes have shape preservation property.
Key wordsPolynomial generation   Continuity   Polynomial reproduction   Fractals   
收稿日期: 2017-12-29; 出版日期: 2019-11-16
基金资助:

国家自然科学基金(61472466,6110012).

引用本文:   
. 一类融合逼近和插值的曲线细分[J]. 计算数学, 2019, 41(4): 367-380.
. A CLASS OF COMBINED APPROXIMATING AND INTERPOLATING SUBDIVISION FOR CURVES[J]. Mathematica Numerica Sinica, 2019, 41(4): 367-380.
 
[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. 浏览
[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. 浏览
[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.
[1] 张迪, 刘华勇, 李璐, 张大明, 王焕宝. 基于几何连续的AT-β-Spline曲线曲面的构造[J]. 计算数学, 2018, 40(3): 227-240.
[2] 郑雄波, 张晓威. 多小波变换在声纳图像降噪中的应用研究[J]. 计算数学, 2011, 32(2): 89-96.
[3] 郑雄波, 张晓威. 一种基于多小波变换的自适应图像插值算法[J]. 计算数学, 2009, 30(3): 211-217.
[4] 杨小远,赵明,李波. 基于IFS系统的快速分形编码算法研究[J]. 计算数学, 2006, 27(2): 114-122.
[5] 赵明,杨小远,李波. 一种优选匹配的快速分形图像编码算法[J]. 计算数学, 2006, 27(1): 24-30.
[6] 李红达,叶正麟,彭国华. Cantor尘的Hausdorff测度估计[J]. 计算数学, 2002, 24(3): 265-272.
[7] 卢建朱. 非均匀分形插值函数的光滑性和Hlder指数[J]. 计算数学, 2000, 22(2): 177-182.
[8] 王烈衡,王光辉. 弹性接触问题的对偶混合有限元分析[J]. 计算数学, 1999, 21(4): 483-494.
[9] 王烈衡,王光辉. 弹性接触问题的一种新的混合变分形式[J]. 计算数学, 1999, 21(2): 237-244.
[10] 江雷,王仁宏. 矩形域与三角域Bezier曲面间的PPG~n变换[J]. 计算数学, 1999, 21(2): 245-250.
[11] 王何宇. 经典分形集测度上估的计算机搜索Ⅰ──对典型例子Sierpinski垫片编码技术的剖析[J]. 计算数学, 1999, 21(1): 109-116.
[12] 王艳春. 一种二次保形插值参数曲面[J]. 计算数学, 1998, 20(2): 121-.

Copyright 2008 计算数学 版权所有
中国科学院数学与系统科学研究院 《计算数学》编辑部
北京2719信箱 (100190) Email: gxy@lsec.cc.ac.cn
本系统由北京玛格泰克科技发展有限公司设计开发
技术支持: 010-62662699 E-mail:support@magtech.com.cn
京ICP备05002806号-10