• 论文 • 上一篇    下一篇

一类新的(2n-1)点二重动态逼近细分

张莉, 孙燕, 檀结庆, 时军   

  1. 合肥工业大学数学学院, 合肥 230009
  • 收稿日期:2016-01-12 出版日期:2017-02-15 发布日期:2017-02-17
  • 基金资助:

    国家自然科学基金重点项目(U1135003);国家自然科学基金(61472466,61100126);中国博士后科学基金面上资助项目(2015M571926);浙江大学CAD、CG国家重点实验室开放课题(A1607).

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.

Zhang Li, Sun Yan, Tan Jieqing, Shi Jun. A NEW FAMILY OF (2n-1)-POINT BINARY NON-STATIONARY APPROXIMATING SUBDIVISION SCHEMES[J]. Mathematica Numerica Sinica, 2017, 39(1): 59-69.

A NEW FAMILY OF (2n-1)-POINT BINARY NON-STATIONARY APPROXIMATING SUBDIVISION SCHEMES

Zhang Li, Sun Yan, Tan Jieqing, Shi Jun   

  1. School of Mathematics, Hefei University of Technology, Hefei 230009, China
  • Received:2016-01-12 Online:2017-02-15 Published:2017-02-17
利用正弦函数构造了一类新的带有形状参数ω的left(2n-1right)点二重动态逼近细分格式.从理论上分析了随n值变化时这类细分格式的Ck连续性和支集长度;算法的一个特色是随着细分格式中参数ω的取值不同,相应生成的极限曲线的表现张力也有所不同,而且这一类算法所对应的静态算法涵盖了Chaikin,Hormann,Dyn,Daniel和Hassan的算法.文末附出大量数值实例,在给定相同的初始控制顶点,且极限曲线达到同一连续性的前提下和现有几种算法做了比较,数值实例表明这类算法生成的极限曲线更加饱满,表现力更强.
In this paper,a new family of (2n-1)-point binary non-stationary approximating subdivision schemes with shape parameter ω is presented with the help of the sine function.With the changing of n and ω,the theoretical analysis of support length and continuities of the schemes are also given.The corresponding stationary schemes include the methods given by Chaikin,Hormann,Dyn,Daniel and Hassan.With the same control points and the same continuities for the limit curves,comparisons with other methods are given.It shows that the new family of schemes can generate limit curves with better representability than the others.

MR(2010)主题分类: 

()
[1] Chaikin G M. An algorithm for high speed curve generation[J]. Comput. Graph. Image Process, 1974, 3(4):346-349.

[2] Hormann K, Sabin M A. A family of subdivision schemes with cubic precision[J]. Comput. Aided Geomet. Des. 2008, 25(1):41-52.

[3] Dyn N, Floater M S, Hormann K. A C2 four-point subdivision scheme with fourth order accuracy and its extensions[J]. in:M. Daehlen, K. Morkenm, L.L. Schumaker (Eds.), Mathematical Methods for Curves and Surfaces:Troms 2004, Modern Methods in Mathematics, Nashboro Press, Brentwood, Tenn, USA, 2005, pp. 145-156.

[4] Tan J Q, Yao Y G, Cao H J. Convexity preservation of five-point binary subdivision scheme with a parameter[J]. Appl. Math. Comput. 2014, 245:279-288.

[5] Dyn N, Gregory J A, Levin D. A four-point interpolatory subdivision scheme for curve design[J]. Comput. Aided Geomet. Des. 1987, 4(4):257-268.

[6] 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.

[7] 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.

[8] Deng C Y, Wang G Z. Incenter subdivision scheme for curve interpolation[J]. Comput. Aided Geomet. Des. 2010, 27(1):48-59.

[9] Deng C Y, Ma W Y. Matching admissible G2 Hermite data by a biarc-based subdivision scheme[J]. Comput. Aided Geomet. Des. 2012, 29(6):363-378.

[10] 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.

[11] Deng C Y, Ma W Y. Efficient evaluation of subdivision schemes with polynomial reproduction property[J]. J. Comput. Appl. Math. 2016, 294(C):403-412.

[12] Schaefer S, Warren J. Exact evaluation of limits and tangents for non-polynomial subdivision schemes[J]. Comput. Aided Geom. Design, 2008, 25(8):607-620.

[13] Dyn N, Levin D. Analysis of asymptotically equivalent binary subdivision schemes[J]. J. Math. Anal. Appl. 1995, 193(2):594-621.

[14] Jena M K, Shunmugaraj P, Das P C. A non-stationary subdivision scheme for curve interpolation[J]. ANZIAM J. 2003, 44(E):E216-E235.

[15] Daniel S, Shunmugaraj P. Three point stationary and non-stationary subdivision schemes[C]//3rd International Conference on Geometric Modeling, Imaging. IEEE, 2008:3-8.

[16] Fang M E, Ma W Y, Wang G Z. A generalized curve subdivision scheme of arbitrary order with a tension parameter[J]. Comput. Aided Geomet. Des. 2010, 27(9):720-733.

[17] 庄兴龙, 檀结庆. 五点二重逼近细分法[J]. 图学学报, 2012, 33(5):57-61.

[18] Siddiqi S S, Rehan K. Modified form of binary and ternary 3-point subdivision schemes[J]. Appl. Math. Comput. 2010, 216(3):970-982.

[19] Siddiqi S S, Salam W, Rehan K. Binary 3-point and 4-point non-stationary subdivision schemes using hyperbolic function[J]. Appl. Math. Comput. 2015, 258(C):120-129.

[20] Cao H J, Tan J Q. A binary five-point relaxation subdivision scheme[J]. J. Inf. Comput. Sci. 2013, 10(18):5903-5910.

[21] Mustafa G, Ghaffar A, Bari M. (2n-1)-point binary approximating scheme[C]//Digital Information Management (ICDIM), 2013 Eighth International Conference on. IEEE, 2013:363-368.

[22] Dyn N, Levin D. Subdivision schemes in geometric modeling[J]. Acta Numerica, 2002, 11:73-144.

[23] Hassan M F, Dodgson N A. Ternary and three-point univariate subdivision schemes[J]. In:Albert Cohen, Jean-Louis Merrien, Larry L. Schumaker (Eds.), Curve and Surface Fitting:Sant-Malo 2002, Nashboro Press, Brentwood, 2003, pp. 199-208.
[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] 李军成, 刘成志. 带两个形状参数的同次Bézier曲线[J]. 计算数学, 2017, 39(2): 115-128.
[3] 刘植, 陈晓彦, 江平, 张莉. 基于函数值的线性有理插值样条的区域控制[J]. 计算数学, 2011, 33(4): 367-372.
[4] 吴荣军, 彭国华, 罗卫民. 一类带参 B 样条曲线的形状分析[J]. 计算数学, 2010, 32(4): 349-360.
阅读次数
全文


摘要