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三角域上保正有理插值曲面的构造 被引量：1

Construction of positivity-preserving rational interpolation surface over triangle
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摘要 对三角域上C1连续的有理样条曲面保正插值的问题进行了研究.应用三角剖分上的有理样条插值曲面重心坐标下的等价形式,由Bézier曲面保正的充分条件得到了有理样条函数系数的约束条件,从而保证了有理样条函数的非负性,该方法是一种局部调整的方法.数值实验表明该算法是可行并且有效的. In this paper, a positivity-preserving rational interpolation scheme is developed. Based on the equivalent form of rational spline on triangulation, the conditions on the coefficients of rational spline are given by the sufficient nonnegativity conditions of Bezier patch. It is a local method. At the end of the paper, numerical examples show the method feasible and effective.
作者 彭兴璇
机构地区 辽宁师范大学数学学院
出处 《辽宁师范大学学报（自然科学版）》 CAS 2009年第2期151-153,共3页 Journal of Liaoning Normal University:Natural Science Edition
基金 辽宁省教育厅科学技术研究项目(2008358)
关键词 有理样条 保正 插值 rational spline positivity-preserving interpolation
分类号 O241.5 [理学—计算数学]
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参考文献9

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同被引文献14

  • 1王文涛,汪国昭.带形状参数的均匀B样条[J].计算机辅助设计与图形学学报,2004,16(6):783-788. 被引量：83
  • 2吴晓勤.带形状参数的Bézier曲线[J].中国图象图形学报,2006,11(2):269-274. 被引量：58
  • 3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
  • 4DUAN Q,BAO F X,DU S T,et al.Local control of interpolating rational cubic spline curves[J].Computer Aided Design,2009,41:825-829.
  • 5BAO F X,SUN Q H,DUAN Q.Point control of the interpolating curve with a rational cubic spline[J],Journal of Communication and Image,2009,20:275-280.
  • 6MALIK Z H,MUHAMMAD S.Shape preserving rational cubic spline for positive and convex data[J].Egyptian Informatics Journal,2011,12:231-236.
  • 7MALIK Z H,HUSSAIN Maria.Visualization of 3D data preserving convexity[J].Math Computing,2007,4:397-410.
  • 8ZHANG Y F,DUAN Q,TWIZELL E H.Convexity control of a bivariate rational interpolating spline surfaces[J],Computers Graphics,2007,37:679-687.
  • 9DUAN Q,DJIDJELI K,PRICE W G,et al.Weighted rational cubic spline interpolation and its application[J],Journal of Compu- tational and Applied Mathematics,2000,117(2):121-135.
  • 10CASCIOLA GiROMANI L.Rational interpolants with tension parameters[M].Brentwood? Nashboro Press,2003:41-50.

引证文献1

辽宁师范大学学报（自然科学版）
2009年 第2期

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