基于参数样条插值的同坡曲面构造方法

A Method for Constructing Identical Slope Surface Based on Parametric Spline Interpolation

传统的同坡曲面构造方法都是在导线方程为已知的前提下进行的。然而在实际工程中,导线方程往往是很难得到的,只能通过测量得知导线通过一列数据点。针对这一问题,给出了一种实际工程中同坡曲面的构造方法,该法首先根据测量数据点,利用三次参数样条曲线插值方法构造出同坡曲面的导线方程,然后再从同坡曲面的形成原理入手建立其参数方程,最后通过实例表明该方法是可行有效的。

The traditional method for constructing identical slope surface is under the premise that exact expression of lead curve is known.But in practical engineering,the exact expression of lead curve is hard to obtain,and only some measured data points of the lead curve are given.For solving that problem,a method of constructing the identical slope surface in engineering is presented in this paper.Firstly,cubic parametric spline interpolation curve is constructed according to the measured data points,which is regarded as the lead curve.Then,the parametric equation of identical slope gradient surface is constructed based on the forming principle of that surface.Lastly,an example is presented to show the method is feasible and effectual.