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一类Hermite型矢量插值C^1细分曲线的几何特征生成 被引量：1

Geometric Features Generation of a Family of Hermite-Type Vector Interpolating Subdivision Schemes
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摘要 通过切矢估计和弦长参数化方法,得到初始Hermite元素序列,定义一类Hermite型矢量插值细分模式。分析了该模式的收敛性和连续性,对满足误差要求的细分迭代层数作出估计,给出达到C1连续的条件。给初始Hermite元素增加附加条件,生成包含直线、尖点、尖角和拐点等特殊几何特征,并生成曲线的细分等距线。 A family of Hermite-type vector interpolating subdivision schemes is proposed and its convergence and continuity are analyzed. The scheme＇s iterative layers are estimated for given error. The necessary and sufficient conditions of C^1 continuity are proved. Geometric features of subdivision curves, such as line segments and cusps etc., are obtained by appending some conditions to initial Hermite elements. An algorithm is presented for generating geometric features and subdivided offset curves.
作者 樊敏 康宝生
机构地区 北京跟踪与通信技术研究所 西北大学计算机科学系
出处 《工程图学学报》 CSCD 北大核心 2006年第3期79-83,共5页 Journal of Engineering Graphics
关键词 计算机应用 计算机辅助几何设计 细分曲线 Hermite元素 HERMITE型 插值细分模式 computer application computer aided geometric design subdivision curves Hermite elements Hermite-type interpolation subdivision schemes
分类号 TP391.72 [自动化与计算机技术—计算机应用技术]
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参考文献2

  • 1Merrien J L. A family of Hermite interpolants by bisection algorithms [J]. Numerical Algorithms, 1992,2: 187-200.
  • 2Dyn N, Levin D. Analysis of Hermite-type subdivision schemes [A]. In: Chui C K, Schumaker (eds) L L.Approximation Theory Ⅷ,Ⅴ. 2: Wavelets and Multilevel Approximation [C]. Singapore: World Scientific, 1995.117-124.

同被引文献12

  • 1张彩明,汪嘉业.可调整C^2四次Bézier插值曲线的构造[J].计算机学报,2004,27(12):1665-1671. 被引量：5
  • 2Ahlberg J H, Nilson E N, Walsh J L. The theory of splines and their applications [M]. New York: Academic Press, 1967: 1.
  • 3Hail X L. A degree by degree recursive construction of Hermite spline interpolants [J]. Journal of Computational and Applied Mathematics, 2009, 225(225): 113-123.
  • 4Zhu Y P, Han X L, Han J, et al. Quartic trigonometric B6zier curves and shape preserving interpolation curves [J]. Journal of Computational Information Systems, 2012, 8(2): 905-914.
  • 5Mtihlbach G One sided Hermite interpolation by piecewise different generalized polynomials [J]. Journal of Computational and Applied Mathematics, 2005, 196(1) 285-298.
  • 6Agarwal R P, Wong P J Y. Error inequalities in polynomial interpolation and their applications [M]. Dordrecht: Kluwer Academic Publishers, 2012: 217-280.
  • 7Kong J H, Jeong S P, Lee S, et al. C1 Hermite interpolation with simple planar PH curves by speed reparametrization [J]. Computer Aided Geometric Design, 2008, 25(4): 214-229.
  • 8Goodman T N T, Shape preserving interpolation by curves [C]//Algorithrns for Approximation W. Huddersfield: The University of Huddersfield Press, 2002: 24-35.
  • 9Yong J H, Cheng F H. Geometric Hermite curves with minimum strain energy [J]. Computer Aided Geometric Design, 2004, 21(3): 281-301.
  • 10HOllig K, Koch J. Geometric Hermite interpolation with maximal order and smoothness [J]. Computer Aided Geometric Design, 1996, 13(8): 681-695.

引证文献1

工程图学学报
2006年 第3期

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