三次均匀B样条曲线的一种新扩展
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摘要
构造了一组带形状参数的三次B样条曲线,该曲线与经典三次B样条曲线具有相同的基本性质,且可在不改变控制顶点的情况下,通过改变形状参数的取值实现对曲线形状的调整;选取适当的控制顶点,并对形状参数选取适当的取值,构造的三次λ-B样条曲线可以很好的逼近圆和椭圆;提供了插值于已知数据点的λ-B样条曲线的构造方法;最后,通过图例体现了新方法的有效性.
The cubic B spline curves with a shape parameter is constructed. The new curves have the same basic properties of cubic B spline curves. Further, the new curves can adjust the shape by changing the value of the shape parameter without changing the control points. On the condition of selecting the appropriate control points and the appropriate value for the shape parameter, the circle and the ellipse are approximated well by the λ-B spline curves. In addition, the construction of the λ-B spline curves which Interpolate the known data points is given. Finally, the validity of the new method is demonstrated through the illustrations.
The cubic B spline curves with a shape parameter is constructed. The new curves have the same basic properties of cubic B spline curves. Further, the new curves can adjust the shape by changing the value of the shape parameter without changing the control points. On the condition of selecting the appropriate control points and the appropriate value for the shape parameter, the circle and the ellipse are approximated well by the λ-B spline curves. In addition, the construction of the λ-B spline curves which Interpolate the known data points is given. Finally, the validity of the new method is demonstrated through the illustrations.
引文
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[2]李军成,谢炜.自动满足C~2连续的带参数的五次Hermite插值样条[J].浙江大学学报:理学版,2016,43(2):175-180.
[3] Han Xuli. Piecewise quartic polynomial curves with a local shape parameter[J]. Journal of Computational and Applied Mathematics, 2006, 19(5):34-45.
[4]李军成,刘成志,易叶青.带形状参数的C~3连续的分段七次Hermite插值曲线[J].计算机辅助几何设计与图形学学报,2017, 29(12):2204-2215.
[5] Han X L. Quadratic trigonometric polynomial curves with a shape parameter[J]. Computer Aided Geometric Design, 2002, 19(7):503-512.
[6]刘成志,李军成.带形状参数的类三次代数三角Hermte样条插值曲线[J].计算机工程与科学,2016,38(7):1479-1483.
[7]谢进,邬弘毅,邓四清,等.多形状参数的二次非均匀三角多项式曲线[J].工程图学学报,2007, 28(5):49-53.
[8]李军成,刘成志·形状可调的C2连续三次三角Hermite插值样条[J].计算数学,2016, 38(2):187-199.
[9]王文涛,汪国昭.带形状参数的双曲多项式均匀B样条[J].软件学报,2005, 16(4):625-633.
[10] Lu Y G, Wang G Z, Yang X N. Uniform hyperbolic polynomial B-spline curves[J]. Computer Aided Geometric Design, 2002, 19(6):379-393.
[11]谢进,檀结庆.多形状参数的二次双曲多项式曲线[J].中国图像图形学报,2009, 14(6):1206-1211.
[12]朱远鹏.基函数中带形状参数的几何造型理论与方法研究[D].长沙:中南大学,2014.
[13] Hoschek J, Lasser D. Fundamentals of Computer Aided Geometric Design[M]. Wellesley, MA:A K Peters, 1993.
[2]李军成,谢炜.自动满足C~2连续的带参数的五次Hermite插值样条[J].浙江大学学报:理学版,2016,43(2):175-180.
[3] Han Xuli. Piecewise quartic polynomial curves with a local shape parameter[J]. Journal of Computational and Applied Mathematics, 2006, 19(5):34-45.
[4]李军成,刘成志,易叶青.带形状参数的C~3连续的分段七次Hermite插值曲线[J].计算机辅助几何设计与图形学学报,2017, 29(12):2204-2215.
[5] Han X L. Quadratic trigonometric polynomial curves with a shape parameter[J]. Computer Aided Geometric Design, 2002, 19(7):503-512.
[6]刘成志,李军成.带形状参数的类三次代数三角Hermte样条插值曲线[J].计算机工程与科学,2016,38(7):1479-1483.
[7]谢进,邬弘毅,邓四清,等.多形状参数的二次非均匀三角多项式曲线[J].工程图学学报,2007, 28(5):49-53.
[8]李军成,刘成志·形状可调的C2连续三次三角Hermite插值样条[J].计算数学,2016, 38(2):187-199.
[9]王文涛,汪国昭.带形状参数的双曲多项式均匀B样条[J].软件学报,2005, 16(4):625-633.
[10] Lu Y G, Wang G Z, Yang X N. Uniform hyperbolic polynomial B-spline curves[J]. Computer Aided Geometric Design, 2002, 19(6):379-393.
[11]谢进,檀结庆.多形状参数的二次双曲多项式曲线[J].中国图像图形学报,2009, 14(6):1206-1211.
[12]朱远鹏.基函数中带形状参数的几何造型理论与方法研究[D].长沙:中南大学,2014.
[13] Hoschek J, Lasser D. Fundamentals of Computer Aided Geometric Design[M]. Wellesley, MA:A K Peters, 1993.