[1]徐少平,刘小平,李春泉,等.均匀B样条1次升降多阶的矩阵表示[J].江西师范大学学报(自然科学版),2012,(03):257-262.
 XU Shao-ping,LIU Xiao-ping,LI Chun-quan,et al.The Matrix Representation for Multi-Degree Reduction or Elevation of Uniform B-Spline Curves[J].,2012,(03):257-262.
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均匀B样条1次升降多阶的矩阵表示()
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《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2012年03期
页码:
257-262
栏目:
出版日期:
2012-05-01

文章信息/Info

Title:
The Matrix Representation for Multi-Degree Reduction or Elevation of Uniform B-Spline Curves
作者:
徐少平;刘小平;李春泉;胡凌燕;杨晓辉
南昌大学信息工程学院,江西南昌330031
Author(s):
XU Shao-ping LIU Xiao-ping LI Chun-quan HU Lin-yan YANG Xiao-hui
关键词:
计算机图形学 B 样条转换矩阵矩阵表示
Keywords:
computer graphic B-spline transformation matrix matrix representation
分类号:
TP391.7
文献标志码:
A
摘要:
研究了均匀 B 样条曲线的1次升降多阶的矩阵表示,提出了将计算过程表示为多个矩阵连续相乘的形式,矩阵的乘积作为 B 样条升降阶的转换矩阵,得到 B 样条曲线升降阶后的控制顶点矢量可以表示为转换矩阵与原曲线控制顶点矢量乘积的形式.该方法不需要使用节点插入、节点删除和节点优化技术,具有模块化、可扩展性、便于实现等优点
Abstract:
Multi-degree elevation and degree reduction of B-Spline curves in a matrix representation was proposed. The control points of the degree elevated or reduced B-Spline curve can be obtained as a product of the transformation matrix and the vector of original control points. The method does not need knots inserting or knots refinment. In this way, the process of degree changing of B-spline simply express.

参考文献/References:

[1] 孙家广, 胡事民. 计算机图形学基础教程 [M]. 2版. 北京: 清华大学出版社, 2011.
[2] Samuel R Buss. 3D computer graphics: a mathematical introduction with OpenGL [M]. Cambridge: Cambridge University Press, 2003.
[3] Eck M, Hadenfeld J. Knot removal for B-spline curves [J]. Computer Aided Geometric Design, 1995, 12(3): 259-282.
[4] Liu W. A simple efficient degree raising algorighm for B-spline curves [J]. Computer Aided Geometric Design, 1997, 14(7): 693-698.
[5] Huang Qixing, Hu Shimin, Martin Ralph R. Fast degree elevation and knot insertion for B-spline curves [J]. Computer Aided Geometric Design, 2005, 22(2): 183-197.
[6] Piegl L, Tiller W. Algorithm for degree reduction of B-spline curves [J]. Computer-Aided Design, 1995, 27(2): 101-110.
[7] Eck M. Least squares degree reduction of Bézier curves [J]. Computer-Aided Design, 1995, 27(11): 845-851.
[8] 秦开怀, 黄海昆. B 样条曲线降阶新方法 [J]. 计算机学报, 2000, 23(3): 306-310.
[9] Yong Junhai, Hu Shimin, Sun Jiaguang, et al. Degree reduction of B-spline curves [J]. Computer Aided Geometric Design, 2001, 18(2): 117-127.
[10] 潘日晶. NURBS曲线曲面的显式矩阵表示及其算法 [J]. 计算机学报, 2001, 24 (4) : 358-366.
[11] Rommani L, Sabin M A. The conversion matrix between uniform B-spline and Bézier representations [J]. Computer Aided Geometric Design, 2004, 21(6): 549-560.
[12] Kim H O, Moon S Y. Degree reduction of Bézier curves by L1-approximation with endpoint interpolation [J]. Computers Math Applic, 1997, 33(5): 67-77.
[13] Kim H J, Ahn Y J. Good degree reduction of Bézier curves using Jacobi polynomials [J]. Computers and Mathematics with Applications, 2000, 40(10): 1205-1215.
[14] Ahn Y J. Using Jacobi polynomials for degree reduction of Bézier curves with Ck-constraints [J]. Computer Aided Geometric Design, 2003, 20(7): 423-434.
[15] Rababah A, Lee B, Yoo J. A simple matrix form for degree reduction of Bézier curves using Chebyshev–Bernstein basis transformations [J]. Applied Mathematics and Computation, 2006, 181(1): 310-318.
[16] Sunwoo Hasik, Lee Namyong. A unified matrix representation for degree reduction of Bézier curves [J]. Computer Aided Geometric Design, 2004, 21(2): 151-164.
[17] Lee B, Park Y, Yoo J. Application of Legendre-Bernstein basis transfromations to degree elevation and degree reduction [J]. Computer Aided Geometric Design, 2002, 19(9): 709-718.
[18] 成敏, 王国瑾. 基于显式矩阵表示和多项式逼近论的NURBS曲线降多阶 [J]. 中国科学: E辑, 2003, 33(8): 673-680.

更新日期/Last Update: 1900-01-01