带形状参数的C^2四次样条曲线

C^2 4-degree continuous spline curves with the shape parameter

提出一类C2连续的带有形状参数的四次样条曲线,曲线上的所有曲线段的控制顶点由给定多边形的顶点直接计算产生。通过改变局部形状参数的取值,可以调整曲线接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。最后实例表明,利用该方法进行曲线设计是有效的。

This paper deals with a class of C^2 4-degree continuous spline curves with some shape parameter. The segmented curves are all shape-preserving to the given polygon. By changing the value of the shape parameter, the approaching degree of the curves to their control polygon can be adjusted. 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 for CAGD.