两条Bézier样条的光滑连接

Smooth Connection between Two Bézier Spline Curves

研究了用一条样条曲线把两条不相连接的样条曲线光滑连接起来的问题,给出了连接两条一元n次参数样条曲线为一条新的一元n次参数样条曲线的条件,适用于参数样条曲线添加控制顶点的情形,进一步得到了两条一次、二次、三次Bézier样条曲线在几何连续性下实现自然光滑连接的条件.

For any two segregated spline curves, the problem of their smooth connection with a spline curve is studied, the condition is given for connecting two univariate parametric splines with degree n into a new univariate parametric spline curves with degree n, it could be used to insert control points of Bézier spline curves, and the conditions is obtained for smooth connection of two Bézier spline curves with respect to degree 1, degree 2 and 3 in geometric continuity.