二次精度参数插值曲线的构造

提出了一种构造三次参数曲线对给定数据点插值的新方法。该方法不同于现有的许多参数曲线构造方法,其构造参数曲线没有选择节点的过程,而是在每2个数据点之间构造一条单位区间上的三次埃尔米特插值曲线段,所有曲线段拼合在一起形成整体的插值曲线,该方法的关键是计算每个数据点处的导矢。对每个数据点,该方法使用5或4个数据点构造一条二次多项式曲线,数据点处的导矢由二次多项式曲线的导矢近似。该方法构造的三次参数曲线具有二次多项式精度。并以以实例对新方法与其它方法构造的插值曲线的精度进行了比较,结果表明,新方法构造的插值曲线的精度较高。

Construction of a parametric cubic curve with quadratic precision

A method for constructing a parametric cubic curve to interpolate a set of distinct data points was presented. Unlike existing methods, this method includes the determination of knots in the process of constructing a parametric curve, and the new method can construct an interpolation curve without the process of determining knots. Between each pair of data points, a cubic Hermite interpolation curve segment was constructed by the new method, and all the curve segments are put together to form the whole interpolation curve. Hence, the key of this new method is to compute the derivative vector at each data point. For each data point, this newmethod constructs a quadratic polynomial curve using five or four data points, and the derivative vector at each data point was computed by the quadratic polynomial curve. The constructed cubic polynomial curve has the precision of the quadratic polynomial. Experiments for testing the efficiency of the new method with the existing ones were included, and comparison results show that the curves by this new method have better precision.