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一种新的带参数双三次有理插值样条的有界性与点控制 被引量：5

BOUNDED PROPERTY AND POINT CONTROL OF A NEW BIVARIATE RATIONAL BICUBIC INTERPOLATING SPLINE WITH PARAMETERS
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摘要 文[19]中,作者构造了一种基于函数值的带参数的分子为双三次、分母为双二次的二元有理插值样条.本文进一步研究该种二元有理插值样条的有界性,给出插值的逼近表达式,讨论插值曲面形状的点控制问题.在插值条件不变的情况下,插值区域内任一点插值函数的值可以根据设计的需要通过对参数的选取修改,从而达到插值曲面局部修改的目的. A bivariate rational interpolation method with parameters was created in an earlier work which was based on function values only, and this spline is with bicubic numerator and biquadratic denominators. This paper will deal with the bounded property, approximation property and the point control method of the interpolating surface. It is proved that the values of the interpolating function in the interpolation region are bounded no matter what the parameters might be. Also, the approximation expression of the interpolation are derived. More important is that the values of the interpolating function at point in the interpolating region can be modified under the condition that the interpolating data are not changed by selecting the suitable parameters, so the interpolation surface can be modified for the given interpolation data when needed in practical design.
作者 邓四清 方逵 谢进 陈福来 陆海波
机构地区 韶关学院数学与信息科学学院 湖南农业大学信息科学技术学院 合肥学院数理系 湘南学院数学系
出处 《计算数学》 CSCD 北大核心 2010年第4期337-348,共12页 Mathematica Numerica Sinica
基金 国家自然科学基金资助项目(60773110) 湖南省教育厅科研资助项目(06C791 09B096) 湖南省科技计划项目(2008FJ3046) 安徽省教育厅自然科研项目(KJ2008B250) 韶关学院校级重点扶持学科建设项目 湖南省重点学科建设项目资助 湖南省高校科技创新团队支持计划资助
关键词 插值 有理样条 有界性 点控制 计算机辅助几何设计 interpolation rational spline bounded property point control computer aided geometric design
分类号 O241.3 [理学—计算数学]
  • 相关文献

参考文献19

  • 1Farin G.Curves and surfaces for computer aided geometric design:A practical guide[M].Academic press,1988.
  • 2Chui C K.Multivariate spline[M].SIAM,1988.
  • 3Bezier P E.The mathematical basis of the UNISURF CAD system[M].Butterworth,London,1986.
  • 4Boor C.A practical guide to splines[M].Revised Edition,Springer-Verlag,New York,2001.
  • 5Wang R H.Multivariate spline functions and their application[M].Science press/Kluwer academic,Beijing,2001.
  • 6Dierck P,Tytgat B.Generating the Bezier points ofβ-spline curve[J].Computer Aided Geometric Design,1989,6(2):279-291.
  • 7Piegl L.On NURBS:A survey[J].IEEE Computer Graphics and Application,1991,11(1):55-71.
  • 8Nielson G M.CAGD's Top Ten:What to watch[C].IEEE Computer Graphics and Automation,1993,35-37.
  • 9Kouichi Konno,Hiroaki Chiyokura.An approach of designing and controlling free-form surfaces by using NURBS boundary Gregory patches[J].Computer Aided Geometric Design,1996,13(4):825-849.
  • 10Laurie M.Wilcox.First and second contributions to surface interpolation[J].Vision Research,1999,39:2335-2347.

二级参考文献31

  • 1邓四清,方逵,谢进.一类基于函数值的有理三次样条曲线的形状控制[J].工程图学学报,2007,28(2):89-94. 被引量：19
  • 2Farin G. Curves and surfaces for computer aided geometric design: A practical guide[M]. Academic press, 1988.
  • 3Chui C K. Multivariate spline. SIAM, 1988.
  • 4Bezier P E. The mathematical basis of the UNISURF CAD system. Butterworth, London, 1986.
  • 5Dierck P, Tytgat B. Generating the Bezier points of β-spline curve[J]. Computer Aided Geometric Design, 1989, 6(2): 279-291.
  • 6Piegl L. On NURBS: A survey[J]. IEEE Computer Graphics and Application, 1991, 11(5): 55-71.
  • 7Nielson G M. CAGD's Top Ten: What to watch[C]. IEEE Computer Graphics and Automation, 1993, 35-37.
  • 8Kouichi K, Hiroaki C. An approach of designing and controlling free-form surfaces by using NURBS boundary Gregory patches[J]. Computer Aided Geometric Design, 1996, 13(4): 825-849.
  • 9Laurie M W. First and second contributions to surface interpolation[J]. Vision Research, 1999, 39: 2335-2347.
  • 10Lin R S. Real-time surface interpolator for 3-D parametric surface machining on 3-axis machine tools[J]. Machine tools and Manufacture, 2000, 40: 1513-1526.

共引文献21

同被引文献31

  • 1彭丰富,韩旭里.一类G^2连续分段四次代数样条[J].计算机辅助设计与图形学学报,2006,18(9):1420-1425. 被引量：5
  • 2巴贾吉,徐国良.局部插值逼近的Ck连续分段实代数曲线[C].计算科学技术会议,普渡大学,美国,1992:92-144.
  • 3莫海宁,赵国辉,等.基于混合凸多边形的S;代数样条[J].计算机辅助设计,2007,39(11):l003-l0ll.
  • 4鲍尔西兹尼等.C2连续代数样条的几何控制[J].计算机辅助几何设计,1998,15(3):161-187.
  • 5彭丰富,韩旭里.一类四次C2连续样条[J].计算机辅助设计与图形学学报,2006,18:1420-1425.
  • 6王文平,乔·巴里.有理二次样条曲线在二次曲面上的插值[J].计算机辅助几何设计,1997,14(3):207-230.
  • 7彭丰富,韩旭里.抛物面上的参数样条[J].计算与应用数学,2009,229(1):183-191.
  • 8Qi Duan, K. Djidjeli, W. G. Price and E. H. Twizell. A rational cubic spline based on functionvalues [J]. Computers Graphics, 1998, 22(4): 479-486.
  • 9Abbas M, Majid A A, Ali J M. Monotonicity-preserving C2 rational cubic spline for monotonedata[J]. Applied Mathematics and Computation, 2012, 219(6): 2885-2895.
  • 10Duan Q, Wang L, Twizell E H. A new weighted rational cubic interpolation and its approxima-tion[J]. Applied mathematics and computation, 2005,168(2): 990-1003.

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二级引证文献4

计算数学
2010年 第4期

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