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基于位矢和切矢约束优化的Bézeier曲线形状修改 被引量：2

Shape Modification of Bézier Curves by Constrained Optimization of Position and Tangent Vector
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摘要 研究了带几何约束的Bézier曲线形状调整问题,给出一种改变控制顶点的约束优化方法.首先针对单参数点切矢约束,给出Bézier曲线形状调整的精确公式;并研究了基于单参数点位矢和切矢约束的问题,最后讨论了多参数点的约束修改问题.数值实例结果表明,用拉格朗日方法能对Bézier曲线的形状进行有效的修改. This paper investigates geometric constrained optimization for shape modification of Bezier curves. For the tangent vector constraint of a single parameter, precise formula is obtained for shape modification of Bezier curve. The shape modification problem with both position vector and tangent vector constraints of a single parameter and multiple parameters are also considered. Practical examples are given to show the efficiency of this proposed method.
作者 韩旭里 任叶庆
机构地区 中南大学数学科学与计算技术学院
出处 《计算机辅助设计与图形学学报》 EI CSCD 北大核心 2008年第9期1191-1195,共5页 Journal of Computer-Aided Design & Computer Graphics
基金 湖南省自然科学基金(08JJ3009)
关键词 BEZIER曲线 形状修改 约束优化 Bezier curves shape modification constrained optimization
分类号 TP391.41 [自动化与计算机技术—计算机应用技术]
  • 相关文献

参考文献8

  • 1Piegl L. Modififying of the shape of rational B-spline. Part 1 : Curves [J]. Computer-Aided Design, 1989, 21(8) : 509- 518
  • 2Flowler B, Bartels R. Constrained-Based curved manipulation [J]. IEEE Computer Graphics and Application, 1993, 13(5): 43-49
  • 3Au C K, Yuen M M F. Unified approach to NURBS curve shape modification [J]. Computer-Aided Design, 1995, 27 (2) : 85-93
  • 4Sanehez R J. A simple technique for NURBS shape modification [J]. IEEE Computer Graphics and Application, 1997, 17(1): 52-59
  • 5Hu S M, Zhou D W, Sun J G. Shape modification of NURBS curves via constrained optimization [C]//Proceedinigs of the CAD/Graphics'99. Shanghai, WenHui Publishers, 1999: 958-962
  • 6HuS M, Li Y F, Ju T, et al. Modifying the shape of NURBS surfaces with geometric constraints [J]. Computer-Aided Design, 2001, 33(12) : 903-912
  • 7徐立,陈玉健,胡毓宁.基于约束优化的Bézier曲线的形状修改(英文)[J].软件学报,2002,13(6):1069-1074. 被引量：10
  • 8夏飞海,吴庆标.基于约束优化的Bézier曲面形状修改[J].中国图象图形学报,2006,11(2):265-268. 被引量：3

二级参考文献13

  • 1Piegl L.Modififying of the shape of rational B-spline.Part 1:Curves[J].Computer Aided Design,1989,21(8):509 ～518.
  • 2Flowler B,Bartels R.Constrained-Based curve manipulation[J].IEEE Computer Graphics and Application,1993,13(5):43 ～49.
  • 3Au C K,Yuen M M F.Unified approach to NURBS curve shape modification[J].Computer Aided Design,1995,27(2):85～93.
  • 4Sánchez R J.A simple technique for NURBS shape modification[J].IEEE Computer Graphics and Applications,1997,17(1):52 ～ 59.
  • 5胡事民,周登文,孙家广.基于约束优化的NURBS曲线形状修改[A].见:99'CAD/图像会议论文集[C],上海:上海文汇出版社,1999:958～962.
  • 6Hu Shi-min,Li You-fu,Ju-tao.Modifying the shape of NURBS surfaces with geometric constraints[J].Computer Aided Design,2001,33(12):903 ～912.
  • 7Piegl, L. Modififying of the shapeof rational B-spline. Part 1: Curves. Computer Aided Design, 1989,21(8):509～518.
  • 8Flowler, B., Bartels, R. Constrained-Based curve manipulation. IEEE ComputerGraphics and Application, 1993,13(5):43～49.
  • 9Au, C.K., Yuen, M.M.F. Unified approach to NURBS curve shape modification.ComputerAided Design, 1995,27(2):85～93.
  • 10Sánchez, R.J. A simple technique for NURBS shape modification. IEEE ComputerGraphics and Applications, 1997,17(1):52～59.

共引文献10

同被引文献25

  • 1王志国,周来水,王小平.一种修改NURBS曲线形状的新方法[J].计算机学报,2004,27(12):1672-1678. 被引量：15
  • 2夏飞海,吴庆标.基于约束优化的Bézier曲面形状修改[J].中国图象图形学报,2006,11(2):265-268. 被引量：3
  • 3王青,柯映林,李江雄.基于力密度方法的NURBS曲线和曲面变形框架[J].机械工程学报,2007,43(3):135-142. 被引量：8
  • 4胡事民,周登文,孙家广.基于约束优化的NURBS曲线形状修改[C]//’99CAD图像会议论文集.上海:上海文汇出版社,1999:958-962.
  • 5Piegl L. Modifying the shape of rational B-splines. Part 1 :curves [ J ]. Computer-Aided Design, 1989, 21 ( 8 ), 509-518.
  • 6Piegl L. Modifying the shape of rational B-splines. Part 2 : sur- faces [ J]. Computer-Aided Design, 1989, 21(9), 538-546.
  • 7Wu Q B, Xia F H. Shape modification of Bzier curves by con- strained optimization [J]. 3oumal of Zhejiang University:Science A, 2005, 6(S1), 124-127.
  • 8Juh6sz I. Weight-based shape modification of NURBS curves [ J]. Computer Aided Geometric Design, 1999, 16 (5), 377- 383.
  • 9Pourazady M, Xu X. Direct manipulations of B-spline and NURBS curves [ J ]. Advances in Engineering Software, 2000, 31(2), 107-118.
  • 10Hu S M, Li Y F, Ju T, et al. Modifying the shape of NURBS surfaces with geometric constraints [ J 1. Computer-Aided Design, 2001, 33(12):903-912.

引证文献2

计算机辅助设计与图形学学报
2008年 第9期

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