可调控C^2连续三次三角多项式样条曲线

A class of modifiable C^2 continuous cubic trigonometric polynomial curve

文章提出一类C2连续带有形状参数的三次三角多项式样条曲线。该曲线对给定的多边形具有保形性,通过改变形状参数的取值,可以局部或整体调整曲线逼近其控制多边形的程度。所得结论具有明确的几何意义,有效增强了控制及表达曲线形状的能力。最后用实例表明了该方法的有效性。

This paper presents a class of C^2 continuous cubic trigonometric polynomial spline curves with some shape parameters. The segmented curves are all shape-preserving to given polygons. By changing the value of the shape parameter, the approaching degree of the curves to their control polygon can be adjusted locally or wholly. The results have definite geometric meanings that are useful for shape modification and representation of curves. Finally, a few numerical examples illustrate that the method given in this paper is effective.