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可调形三次三角Cardinal插值样条曲线

宋爱平, 陶建明, 易旦萍, 张益汉   

  1. 扬州大学机械工程学院, 江苏扬州 225127
  • 收稿日期:2014-01-10 出版日期:2015-02-15 发布日期:2015-03-10

宋爱平, 陶建明, 易旦萍, 张益汉. 可调形三次三角Cardinal插值样条曲线[J]. 计算数学, 2015, 37(1): 34-41.

Song Aiping, Tao Jianming, Yi Danping, Zhang Yihan. CUBIC TRIGONOMETRIC CARDINAL INTERPOLATION SPLINE WITH ADJUSTABLE SHAPE[J]. Mathematica Numerica Sinica, 2015, 37(1): 34-41.

CUBIC TRIGONOMETRIC CARDINAL INTERPOLATION SPLINE WITH ADJUSTABLE SHAPE

Song Aiping, Tao Jianming, Yi Danping, Zhang Yihan   

  1. College of Mechanical Engineering, Yangzhou University, Yangzhou 225127, Jiangsu, China
  • Received:2014-01-10 Online:2015-02-15 Published:2015-03-10
在三次Cardinal插值样条曲线的基础上,引入了三角函数多项式,得到一组带调形参数的三次三角Cardinal样条基函数,以此构造一种可调形的三次三角Cardinal插值样条曲线.该插值样条可以精确表示直线、圆弧、椭圆以及自由曲线,改变调形参数可以调控插值曲线的形状.该插值样条避免了使用有理形式,其表达式较为简洁,计算量也相对较少,从而为多种线段的构造与处理提供了一种通用与简便的方法.
By introducing trigonometric polynomial functions on the basis of cubic Cardinal interpolation spline curve, a set of primary functions with shape adjustable parameter is obtained, and a new curve called cubic trigonometric Cardinal interpolation spline is constructed by it. The spline can be used to accurately represent line, arc, ellipse and free curve, and the shape of interpolation spline can be controlled by changing the adjustable parameter. The interpolation spline has a more concise expression by avoid using rational form, and it needs relatively less calculation, which provides a common and simple method for constructing and processing of curves.

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