一种G2连续的二次曲线样条插值方法

给出了一种用二次曲线段来插值平面有序数据点列的一种方法 .文中的曲线采用隐函数表示而不是常用的参数形式 .曲线不是用通常的二曲线方程来表示 ,而是用一种带参数的函数样条来表示 .首先给出用二次曲线来插值两点、两切线以及在一端点处的曲率达到给定值 ;其次 ,给出了用二次曲线样条插值平面上一个有序点列且使曲线达到整体 G2 连续 ;最后就用二次曲线对平面闭曲线插值问题进行了研究 .该方法对数据点列没有任何限定性要求 ,无论是闭曲线还是开曲线 ,都能达到整体 G2连续 .

Interpolating 2D Data Set by Conic Spline with G2 Continuity

A method for interpolating 2D data with conic spline is introduced. The conic is represented by implicit equation. First, a method for interpolating two given end points as well as two given tangents at these points and a given curvature at an end point is presented; Second, a method for interpolating an open points sequence in a plane is offered; Last, a method for interpolating a closed points sequence in a plane is given. The method is very robust for any 2D data sequences. Overall G 2 continuity is held whether the data set is open or closed.