两条样条曲线的光滑连接问题

On smooth connection between two spline curves

为了解决用一条样条曲线把两条不相连接的样条曲线曲面光滑连接起来的问题,根据两个n次样条函数的光滑连接和样条曲线几何光滑连接之间的关系,结合由插值节点确定样条函数的方法和确定光滑样条曲线的条件进行分析处理,得到了两条二次、三次Bézier样条曲线的几何光滑连接的充分条件。这种连接可以通过添加合适的控制点实现。这些方法可以有效地解决两条样条曲线的光滑拼接问题。这个过程中,可以通过改变控制点的数量来调整连接曲线的形状。

To deal with the problem of connecting two segregated spline curves smoothly, we consider the relationship between determining spline by interpolation points and connecting tow spline curves, and propose a sufficient condition for connecting two unvaried parametric spline curves with degree two or three into a new unvaried parametric spline curve. It can be done by inserting control points of spine curves. These methods can be used to solve the problem of smooth connection of two Bězier curves with respect to degree 2 and 3 in geometric continuity. And it could be also used to change the form of connection curve by changing the control porints.