用隐式多项式平面曲线拟合数据点

To Fit Data Point with Implicit Polynomial polynomial 2D Curves

本文提出了一种方法 ,用隐式多项式曲线拟合数据点 ,使数据点到多项式曲线的距离控制在相对较小的范围内。将拟合问题中非线性的目标函数和约束条件转化成线性的形式 ,利用线性规划原理 ,求出逼近于数据点的隐式多项式。该方法不需要求出原始数据点处的导数 ,具有简单、可靠。

In this paper a method is proposed to fit data point with implicit polynomial 2D curves,to make the distance from the data points to the curve within the relatively smaller range. We change the nonlinear restrictions and objective function into their linear form as to coefficients of implicit polynomial, and work out the implicit polynomial approximated to the data points. This method is simple, robust and fast without requirement of derivatives provided by data points.