带多个形状参数的三次均匀B样条曲线的扩展

摘要

通过构造两类带多个形状参数的调配函数,生成三次均匀B样条基函数的扩展.基于给出的调配函数定义了两类带多个形状参数的分段多项式曲线.这些曲线具有三次均匀B样条曲线的绝大多数重要性质,能达到GC1或GC2连续.改变形状参数的值可以独立地调控各子段的端点的位置及其切矢的长度,对曲线进行整体或局部调整,甚至直接插值任何所需的控制点.%Two classes of blending functions with multiple shape parameters are presented in this paper. They are the extension of uniform cubic B-spline basic functions. Based on the given blending functions, the piecewise polynomial curves with shape parameters are defined. These curves inherit the most properties of uniform cubic B-spline curves with GCl or GC2 continuity.The position and the length of tangent vector at the end points of curve segments can be independently controlled by changing the values of the shape parameters. These curves can be adjusted totally or locally and interpolated by any given control points.