二次均匀B样条方法的扩展及其应用

An Extension of the Quadratic B-Spline and Its Application

以经典的二次B样条曲线结构构造了一种带两个形状参数的可调三次多项式曲线.曲线在两个参数变化下最少保证一阶连续,在形状参数取某些特殊值时曲线可以生成二次均匀B样条曲线,插值各控制点的插值样条曲线等等.还可以通过改变形状参数的取值,调整曲线接近控制多边形的程度,也可以调整曲线从两侧逼近二次均匀B样条曲线.还分析了曲线端点位置和切矢的性质以及形状参数变化下对它们的影响,给曲线的形状调整带来一定的指导.最后给出了一些曲线曲面生成及调整的实例.

A methed of generating piecewise cubic polynomial curves with two shape parameters is presented, based on the structure of the quadratic uniform B-Spline curves. For any given values of the two shape parameters, the generated curves can be, at least, one-order continuous. This method can generate quadratic uniform B-Spline curves, interpolation curves that interpolate the control vertices in order and other curves, when some special values of the parameters are given. The properties of the endpoints of the generated curves and their fluctuations under the influence of parameters＇ changing are also analyzed in this paper, which can give some guidelines in the shape modifying of curves. And some illustrations of curves generating and shape modifying are presented.