平面四点确定一条抛物线及其在参数插值中的应用

本文讨论了用平面有序四点确定一条抛物线及其在参数插值中的应用。提出了有用四点确定一条抛物线的算法，讨论了确定抛物线的四点相互间要满足的位置。对平面给定的一组数据点，提出了构造参数插值曲线的新方法。所构造的插值曲线是ＧＣ＾１连续的分片三次参数曲线，其插值精度为二次参数多项式。本文还以计算实例对新方法与其它方法的插值精度进行了比较。

DETERMINING A PARABOLA WITH FOUR ORDERLY POINTS AND ITS APPLICATION IN PARAMETRIC INTERPOLATION

This paper discusses the problem of determining a parabola with four orderly planar points and its application in parametric interpolation. A method of determining a parabola with four points is presented and the position relations which the four points have to satisfy is studied. A method of constructing parametric curve to interpolate a set of planar data points is also presented. The constructed curve is GC1 piecewise parametric cubic polynomial, and it reproduces a parametric polynomial of degree two or less exactly. Experiments for comparing the efficiency of the new method with other methods are also included.