一种<i>G</i><sup>2</sup>连续的二次曲线样条插值方法

一种G²连续的二次曲线样条插值方法

摘要: 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.

Abstract: 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 G² continuity is held whether the data set is open or closed.